LfBRARf 


SCIENTIFIC  THEISM 

Versvt 

MATERIALISM 


SCIENTIFIC  THEISM 

VERSUS 

MATERIALISM 

THE    SPACE-TIME   POTENTIAL 

BY 

ARVID   REUTERDAHL 

DEAK    OF  THE   DEPARTMENT    OF    ENGINEERING    AND   ARCHITECTURE, 
THE    COLLEGE    OF    ST.    THOMAS 


NEW  YORK 
THE  DEVIN-ADAIR  COMPANY 

1920 


Copyright,  1920,  by 
THE  DEVIN-ADAIR  COMPANY 


All  Rights  Reserved  by 
THE  DEVIN-ADAIR  COMPANY 


TO 
MY   WIFE 

ELINOR  LOUISE 

THIS  BOOK  IS  AFFECTIONATELY 

DEDICATED    IN     RECOGNITION    OF    THE 

UNTIRING       INTEREST       AND 

ENCOURAGEMENT      THAT 

ACCOMPANIED     ITS 

DEVELOPMENT 


PREFACE 

HERMANN  LOTZE,  one  of  the  most  profound  philosophers 
of  recent  and  of  all  times,  beginning  with  the  idea  of  inter- 
action, develops,  in  his  work,  a  system  of  philosophy  termed 
"Spiritualistic  Monism"  by  Dr.  Harald  Hoffding.  The 
author  accepts  only  the  initiatory  portion  of  the  Lotzian  con- 
cept of  interaction,  and  develops  it  from  the  standpoint  of 
physical  science  to  its  ultimate  negatory  conclusion  in  his 
Theory  of  Interdependence.  A  total  negation  of  action, 
change,  and  becoming  is  the  final  result  of  this  System  of 
Complete  Relativity.  The  actual  facts  of  cosmic  activity 
and  becoming  necessitate  the  dissolution  of  this  negation 
by  a  Transcendent  and  Immanent  Activity  Principle.  All 
the  cosmic  elements  are  activity  elements.  This  is  true  of 
energons,  vitons,  and  souls,  but  actual  interdependent  inter- 
action of  these  elements  is  possible  only  through  the  abiding 
Eternal  Life  of  the  Absolute  Principle.  This  is,  in  brief, 
what  the  author  has  named  "Scientific  Theism." 

The  author  extends  his  sincere  appreciation  to  Dr.  E. 
Lee  Heidenreich,  the  eminent  consulting  engineer,  mathema- 
tician, and  philosopher  of  Kansas  City,  Missouri,  for  his 
keen  and  encouraging  interest  in  this  work. 

In  the  year  1896,  the  writer  conceived  his  Theory  of 
Interdependence  as  a  System  of  Complete  Cosmic  Relativity 
requiring  an  Absolute  Principle  for  the  resolution  of  its 
paradoxical  negations.  In  the  same  year  he  formulated  the 
fundamental  theses  upon  which  this  work  rests.  Basic 
amongst  these  theses  was  the  conception  that  the  laws  of 
the  primordial  activity  ultimates  or  particles  are  also  the 
laws  of  the  entire  physical  universe.  Consequently  we 
should  be  able  to  pass  uninterruptedly  from  the  activities 
of  the  sub-atomic  particles  to  the  behavior  of  such  great 
material  aggregates  as  planets.  As  an  auxiliary  or  comple- 
mentary thesis  the  writer  held  that  the  physical  universe 
is  composed  of  matter,  and  not  of  a  combination  of  matter 
and  ether.  Therefore  the  writer  regarded  the  ether  medium 

5 


6  PREFACE 

as  a  mathematical  myth.  Because  of  his  Theory  of  Inter- 
dependence and  his  views  that  Space  and  Time  are  Forms 
of  Apprehension,  the  thesis  of  Action  At  A  Distance  fol- 
lowed as  a  logical  consequent.  The  first  published  state- 
ment of  these  views  appeared  April  5,  1902,  in  the  Trans- 
actions of  the  American  Electrochemical  Society  under  the 
caption  "The  Atom  of  Electrochemistry."  The  greater  por- 
tion of  the  mathematical  analysis  was  completed  in  the 
year  1904,  except  that  portion  which  refers  to  the  develop- 
ment of  the  Keplerian  laws,  which  was  completed  in  Septem- 
ber, 1914.  In  the  year  1915  the  author  gave  his  lecture 
entitled  "The  Space-Time  Potential"  at  the  Kansas  State 
Agricultural  College  and  at  the  University  of  Kansas. 

This  work  will  not  have  proved  in  vain  if  it  in  some 
measure  helps  to  inaugurate  an  era  in  which  science,  phi- 
losophy, and  religion  will  constitute  the  invincible  unitary 
triune  guiding  the  soul  in  its  search  for  Absolute  Truth  and 
Perfection. 

ARVID  REUTERDAHL. 
September,  1920. 


CONTENTS 
SYNOPSIS Page  9 

CHAPTER  PAGE 

I  INTRODUCTORY  SUMMARY      ...      15 

II  SOME    INCONSISTENT    CONCEPTS    OP 

MODERN  SCIENCE 45 

III  ACTION   AT   A   DISTANCE   AND   THE 

ETHER  HYPOTHESIS     ....      57 

IV  THE  PROBLEM  OF  A  PHYSICAL  SUB- 

STRATUM       92 

V  THE  MODEL  OP  THE  PHYSICAL  UNI- 

VERSE ACCORDING  TO  THE  SPACE- 
TIME  POTENTIAL 121 

VI  NON-NEWTONIAN    DYNAMICS.     THE 

TRUE  RELATION  BETWEEN  STATICS 
AND  DYNAMICS 145 

VII  SOME  APPLICATIONS  OF  THE  SPACE- 

TIME  POTENTIAL 160 

VIII  ELECTROLYTIC  IONIZATION  AND  CELL 

ACTION        182 

IX  THE  FOUR  WORLDS 191 

7 


8 


CONTENTS 


APPENDIX  A    A  NON-NEWTONIAN  DEVELOPMENT  OF 

THE  PLANETARY  ORBITS    .     .     .     207 

APPENDIX  B  ELECTRICAL  RELATIONS  ACCORDING  TO 
THE  DYNAMICS  OF  THE  SPACE-TIME 
POTENTIAL  228 

APPENDIX  C    CALCULATIONS  INVOLVING  HYPERBOLIC 

LOGARITHMS 253 

APPENDIX  D  THE  SECONDARY  FUNCTION  OF  THE 
SPACE-TIME  POTENTIAL,  AND  THE 
ELECTRICAL  CHARGE  257 


APPENDIX  E 


ELECTROLYTIC  IONIZATION.  THE 
KAUFMANN  EFFECT.  THE  RELA- 
TION OF  WORK  Loci  TO  THE  ATOMIC 
STRUCTURE  AND  DIAMETER.  Avo- 
GADRO'S  CONSTANT.  THE  SPACE- 
TIME  POTENTIAL  THEORY  OF  LIGHT 
SUBSTANTIATED  BY  RECENT  ASTRO- 
NOMICAL OBSERVATIONS  264 


APPENDIX  F  INTERDEPENDENT  AND  INDEPENDENT 
MOTION.  THE  INTERACTION  COEFFI- 
CIENTS. SOME  BASIC  FALLACIES  OF 
PARTIAL  RELATIVITY.  273 


SYNOPSIS 

1.  This  work  is  a  unification  of  science,  philosophy,  and 
religion.    The  fundamental  truths  of  religion  are  derived 
philosophically  from  the  facts  of  science. 

2.  The  "Theory  of  Interdependence"  (first  conceived  in 
the  year  1896,  and  enunciated  in  the  year  1902)  is  universal 
and  complete,  whereas  the  so-called  "Theory  of  Relativity" 
is  particular  and  partial. 

3.  Interdependence  is  the  universal  relativity  of  all 
action.     It  is  complete  mutual  interaction  in  the  entire 
cosmos.    The  "Theory  of  Relativity"  follows  from  the  geo- 
metrical relations  pertaining  to  the  sides  of  a  right  triangle 
in  conjunction  with  the  time  form.    These  relations  are  then 
imposed  upon  physical  phenomena.    The  "Theory  of  Inter- 
dependence" begins  with  the  facts  of  physical  action  and 
concludes  that  every  scientific  statement  concerning  phy- 
sical activity  is  merely  a  relative  statement  which  contains 
no  absolute  explanation. 

4.  The  Theory  of  Interdependence  of  the  Space-Time 
Potential  regards  space  and  time  as  relative  measuring 
standards   of   possible    (potential)    and    actual    (kinetic) 
motion  and  action.    From  the  standpoint  of  the  physical 
universe  numbers  are  mere  ratios  and  have  only  interde- 
pendent or  relative  significance.    Physical  values  are  com- 
posites consisting  of  numbers  together  with   arbitrarily 
chosen  physical  units  of  well  defined  interdependent  or  rela- 
tive dimensions.     According  to  the  Space-Time  Potential 
all  physical  magnitudes  and  values  are  interdependent  and 
interrelated.    Paradoxical  as  it  may  seem,  this  fact  of  com- 
plete interdependence  of  physical  magnitudes  is  the  basic 
and  sufficient  reason  for  their  complete  independence  of  the 
actual  physical  dimensions  arbitrarily  adopted  for  the  units 
of  measurement.    The  second  and  complementary  paradox 
to  the  above,  and  depending  upon  it,  is  that  all  physical 
values  are  constants  or  series  of  constants.     If  physical 
values  were  variable,  we  should  have  chaos  instead  of  cos- 

9 


10  SYNOPSIS 

mos.  A  so-called  physical  variable  is  merely  a  series  of 
physical  constants,  in  which  each  constant  in  the  series 
depends  for  its  value  upon  the  governing  conditions  existing 
at  the  place  and  time  of  observation.  Consequently 
physical  values  are  invariable  magnitudes  because  they 
are  ratios  which  are  independent  of  the  actual  dimen- 
sions of  the  chosen  physical  units  of  measurement. 
Therefore  a  physical  value  is  a  fact  and  not  a  mere  mathe- 
matical speculation.  The  third  paradox  is  that,  although 
physical  values  are  constants,  nevertheless,  taken  in  toto 
for  the  entire  cosmos,  they  are  interdependent  because  of 
the  fact  that  they  are  defined  ad  infinitum  in  terms  of  each 
other.  This  constitutes  a  complete  and  universal  interde- 
pendence and  relativity  which  forces  us  beyond  the  inter- 
dependent unitary  system  called  the  cosmos  if  we  wish  to 
find  the  actuating  principle  which  is  capable  of  transform- 
ing an  otherwise  dead  and  inert  system  into  an  operative 
and  intelligible  cosmos. 

5.  The  constant  values  which  pertain  to  the  interde- 
pendent physical  magnitudes  located  within  an  area  equal 
to  one  ten-thousand-millionth  of  an  inch  exemplify  the  Laws 
of  the  Space-Time  Potential  with  the  same  invariable  rigor 
as  obtains  in  the  case  of  interdependent  physical  magnitudes 
found  within  an  area  equal  to  ten  thousand  million  square 
miles.    This  constitutes  the  complete  relativity  of  physical 
action  (kinetic  or  potential)  to  space  and  time. 

6.  This  work  proves  conclusively  that  the  ether  medium 
is  a  mathematical  myth.    These  conclusions  were  verified 
experimentally  by  the  astronomical  observations  of  May, 
1919,  which  showed  that  light  rays  behave  like  material 
particles,  being  deflected  by  the  sun's  interaction  when 
passing  relatively  close  to  its  surface. 

7.  The  fundamental  Newtonian  concept  of  universal 
gravitation  is  regarded,  in  this  work,  as  a  particular  case  of 
universal  interaction  in  an  interdependent  system.    Newton 
derived  the  Keplerian  Laws  by  a  complete  abandonment  of 
his  own  concept  of  universality.     In  this  work  the  New- 
tonian form  of  the  gravitational  expression  has  been  aban- 
doned, supplanting  it  with  its  anti-differential  in  conformity 
with  the  readily  verifiable  facts  of  the  dynamics  of  bodies 
and  sub-atomic  particles.    In  other  words,  universal  inter- 


SYNOPSIS  11 

action  is  mathematically  describable  in  terms  of  the  inverse 
first  power  of  the  distance,  whereas  the  norm  of  the  New- 
tonian law  of  gravitation  is  the  inverse  second  power  of  the 
distance.  In  this  connection  it  is  noteworthy  that  the  mass 
of  a  sub-atomic  particle  is  inversely  proportional  to  its  radial 
distance^  By  means  of  this  important  modification  we 
accomplish  the  complete  unification  of  the  heretofore 
sharply  differentiated  worlds  of  physical  atoms  and  bodies. 
This  unification  avoids  the  necessity  of  one  set  of  laws  for 
the  behavior  of  atoms  and  sub-atoms  and  another  set  of 
laws  pertaining  to  the  activities  of  molecules,  bodies,  and 
planets. 

8.  Interdependent  interaction  involves  action  and  reac- 
tion in  conformity  with  the  relative  potential  which  pertains 
to  the  involved  work  loci. 

9.  Interdependent  interaction  involves  action  at  a  dis- 
tance between  all  primordial  material  particles  and  their 
aggregates. 

10.  An  action  center  or  kern  is  a  mass-acceleration 
kern.     Mass  regarded  as  an  independent  entity  does  not 
exist.     Matter  is  composed  of  activity  kerns,  or  centers, 
undergoing  change  in  accordance  with  the  laws  of  inter- 
dependence and  interaction.    Mass  independent  and  sepa- 
rated from  acceleration  is  not  a  physical  reality.    Accelera- 
tion apart  from  an  action  kern  is  merely  a  mathematical 
concept  void  of  physical  reality. 

11.  The  principle  of  interdependent  interaction  involves 
the  existence  of  primary  and  secondary  matter.     Physical 
phenomena  consist  in  the  interaction  of  primary  and  sec- 
ondary matter  and  their  aggregates.    Every  physical  action 
involves  an  excitant  and  a  concurrent  material  system.    The 
monon  is  the  primordial  activity  center.    The  energon  is  a 
neutral  gyratory  group  composed  of  monons.    The  neutral 
energon  is  capable  of  change  in  a  twofold  manner,  through 
infinitesimally  minute  gradations,  to  a  high  phase  becoming 
an  electron,  and  to  a  low  phase  becoming  a  positon.    Pri- 
mary matter  is  matter  in  the  neutral  phase.     Secondary 
matter   is   matter   appearing   as   electrons   and   positons. 
Gravitation  is  one  form  of  interaction  between  molecular 
aggregates  composed  of  groups  of  these  ultimates. 

12.    In  the  organic  world  the  primordial  ultimate  is  the 


12  SYNOPSIS 

viton.  The  principle  of  life  is  manifested  in  the  viton.  The 
viton  is  an  elementary  soul,  lacking  that  potentiality  which 
insures  development  into  the  highest  form  of  conscious  life. 
An  organic  center  is  the  result  of  interaction  between  the 
primary  activity  of  the  viton  and  the  secondary  activity  of 
secondary  matter.  God's  ever  present  immanence  insures 
to  every  organism  an  elementary  soul  or  viton  which  is  in 
harmony  with  its  being. 

13.  The  unitary  conscious  center  arises  through  the  con- 
junction and  interaction  of  a  primary  and  a  secondary 
activity.    The  primary  activity  is  the  soul,  which  is  capable 
of  manifesting  the  principle  of  free  individuality.    The  sec- 
ondary activity  is  composed  of  highly  developed  organic 
systems  capable  of  minute  shades  of  responsive  interaction. 
The  soul  is  of  God  through  an  act  of  creation. 

14.  Number  alone  is  incapable  of  accounting  for  the 
great  diversity  of  existence  types  in  the  cosmos.  The  ma- 
terial primordials  are  endowed  by  a  creative  act  of  God 
with  deterministic  character.    The  so-called  laws  of  nature 
are  records  of  the  characteristic  behavior  of  these  pri- 
mordials. 

15.  The  phenomenon  of  light  is  a  case  of  interaction 
between  an  excitant  and  a  concurrent  material  system. 
The  velocity  of  light  is  a  constant  equal  to  the  ratio  of  the 
velocities  of  the  two  systems.    The  truth  of  the  former  con- 
tention has  been  proved  by  the  recent  astronomical  observa- 
tions mentioned  above.    The  latter  deduction  is  in  complete 
conformity  with  the  Michelson  experiment. 

16.  The  variation  in  the  magnitude  of  an  activity  kern 
with  the  variation  of  its' velocity  follows  as  a  direct  conse- 
quence of  the  work  law  of  the  Space-Time  Potential. 

17.  The  atom  of  the  Space-Time  Potential  is  composed 
of  concentric  work  loci   containing   sub-atomic   particles 
existing  in  phases  ranging  from  the  maximum  radial  (the 
electron)  to  the  minimum  radial  (the  positon)  as  we  pass 
from  the  outside  toward  the  center  of  the  atom.     This 
atomic  model  provides  the  necessary  constituent  variants 
to  account  for  the  spectrum. 

18.  Reality  may  be  distinguished  as  absolute  and  rela- 
tive.   These  two  forms  of  reality  are  not  identical  but  inter- 
related.   Our  theory  of  interdependence  regards  God  as  the 


SYNOPSIS  13 

Absolute  Reality,  upon  whom  the  relative  reality  of  the  cos- 
mos depends  for  its  maintenance  and  continuous  existence. 
The  cosmos,  regarded  from  the  physical  standpoint  only,  is 
a  relativity  system  devoid  of  an  Absolute  Principle.  As 
such  the  physical  universe  is  inert  and  inoperative.  This  is 
the  ultimate  philosophy  of  despair  and  pessimism.  The 
relativity  of  interdependence  finds  its  resolution  and  com- 
pletion in  the  Absolute  Principal  of  Activity,  God.  This 
is  the  philosophy  of  assurance  and  optimism.  The  theory 
of  physical  interdependence  results  in  an  inert  and  inactive 
cosmos  unless  this  unitary  inert  system  is  related  to  the 
Absolute  Activity  Principle,  known  to  religion  as  God. 
Such  a  system  of  physical  relativity  ends  with  an  ultimate 
negation  of  all  physical  action.  The  actual  facts  of  physical 
action  force  the  resolution  of  incompleteness  into  com- 
pleteness through  the  Life  Activity  of  God.  The  complete 
theory  of  interdependence  therefore  includes  the  Absolute 
(God)  as  the  physically,  philosophically,  and  religiously 
necessary  complement  to  the  otherwise  unintelligible  and 
inoperative  relativity  system  of  the  cosmos.  Therefore 
physical  interdependence  becomes  the  greatest  proof  of  the 
existence  of  God,  in  whom  the  riddle  of  relativity  finds  its 
answer  and  resolution. 


CHAPTER  I 
INTRODUCTORY  SUMMARY 

1.  God  and  the  Mechanical  Model. 

Can  science  arrive  at  a  consistent  operative  mechanical 
model  of  the  universe  without  including  the  concept  of  God  ? 
We  answer  this  question  with  an  emphatic  No !  Can  a  con- 
sistent operative  model  of  the  universe  be  derived  by  the 
introduction  of  the  concept  of  God?  This  question  we 
answer  with  an  equally  emphatic  Yes !  The  writer  presents 
his  discussion  of  these  questions  in  the  following  chapters. 
The  present  chapter  constitutes  a  synopsis  of  our  position 
freed  from  its  mathematical  developments. 

2.  Pure  Mechanism  Futile. 

When  science,  philosophy,  and  religion  are  placed  to- 
gether in  the  melting-pot  of  reason  the  result  is  the  refuta- 
tion of  materialism.  The  scientific  materialist  denies  the 
validity  of  the  result  for  the  reason  that,  for  him,  two  of 
the  ingredients  in  the  melting-pot  are  worthless ;  philosophy 
is  mere  fantastic  speculation,  and  religion  is  naught  but  an 
emotional  phenomenon  having  its  root  in  superstition. 
Materialists  ignore  the  fact  that  every  branch  of  science  has 
its  empirical  and  its  speculative  components ;  the  empirical 
dealing  with  experimental  facts,  and  the  speculative  dealing 
with  the  mathematical  interpretation  of  these  facts  in  terms 
of  such  scientific  concepts  as  molecules,  atoms,  electrons, 
force  and  energy.  We  propose  to  show  that  speculative 
science,  dealing  as  it  does  mathematically  in  concepts  and 
"convenience  unknowns,"  fails  utterly  in  its  attempt  to 
construct  a  real  world  because  of  its  refusal  to  admit  the 
philosophical  and  religious  interpretations  of  the  world  as 
a  valid  contribution  to  knowledge.  In  the  following  it  will 
be  shown  that  the  concepts  of  science  are  unintelligible, 
inconsistent,  and  ineffective  without  the  fundamental  and 

15 


16  SCIENTIFIC  THEISM 

basic  assumption  of  the  existence  of  a  rational,  teleological, 
and  purposive  activity  principle  which  unifies  and  vitalizes 
all  reality  into  an  ordered  intelligible  cosmos.  Without  the 
concept  of  God  the  conscious  and  the  unconscious  world 
become  unintelligible.  A  mechanistic  theory  of  the  uni- 
verse based  upon  mere  materialistic  concepts  is  rationally 
impossible.  A  mechanistic  theory  of  the  cosmos,  grounded 
in  the  concept  of  God,  and  including  teleology  and  purpose, 
is  not  alone  rationally  possible,  but  is  the  only  theory  which 
is  consistent  with  fact.  Such  a  mechanistic  theory  of  the 
world  is  in  agreement  with  empirical  science,  conforms 
with  the  results  of  philosophical  reflection,  and  satisfies  the 
demands  of  the  religious  consciousness.  In  other  words, 
such  a  mechanistic  world  is  an  ordered  spiritual  cosmos, 
and  not  an  irrational  materialistic  chaos.  The  physical  uni- 
verse becomes  intelligible  as  a  sublime  and  divine  machine 
of  wondrous  potentiality,  complexity,  and  diversity,  vital- 
ized by  an  eternal  rational  purpose.  The  phenomenal 
world  is  a  manifestation  of  God  in  a  Space-Time  Potential. 

3.     Basic  Principles. 

The  two  principal  tasks  confronting  us  are:  first,  to 
show  that  the  concepts  of  materialistic  science  are  invalid 
and  inconsistent  because  of  their  failure  to  include  a 
rational,  selective  and  purposive  activity  principle  as  their 
basic  common  element;  and,  second,  to  present  a  physical 
model  of  the  universe  which  owes  its  ultimate  significance 
and  operativeness  to  that  Eternal  Being  known  to  the  reli- 
gious consciousness  as  God.  A  candid  and  unbiased  analy- 
sis of  the  data  of  empirical  science,  taken  in  conjunction 
with  its  speculative,  hypothetical  and  interpretative  sub- 
structure, forces  us  to  accept  the  validity  of  the  following 
basic  principles : 

1.  The  immanence  of  Divine  Intelligence  throughout  the 
universe. 

2.  The  cosmos  as  a  unitary,  interacting,  rational,  pur- 
posive and  teleological  system. 

It  follows  that  the  physical  universe  is  a  finite  projection 
of  the  Infinite  in  Space  and  Time,  not  independent  of,  but 
totally  dependent  upon,  the  immanence  of  God.  The  cosmos 
is  a  part  of  the  infinite  potentiality  of  God  made  actual  in 


SCIENTIFIC  THEISM  17 

a  finite  manifestation  in  space  and  time  and  in  accordance 
with  causation.  The  Space-Time  Potential  is  that  dynamic 
chart  in  which  the  eternal  potentiality  of  the  Spirit  of  God 
phenomenally  manifests  itself.  It  also  follows  that  the  phy- 
sical universe,  being  a  rational  system,  may  be  interpreted 
mathematically  as  a  system  exhibiting  law  and  uniformity. 
A  mechanistic  model  for  this  system  may  be  conceived. 
The  model  is  inoperative  unless  the  validity  of  the  first 
principle  be  assumed,  and  it  is  totally  inadequate  without 
the  admission  of  the  truth  of  the  second  principle.  More- 
over, physico-chemical  forces  are  mere  mathematical  ex- 
pressions devoid  of  a  genuine  activity  principle  unless  both 
of  the  above  premises  are  admitted  as  true.  Consequently 
the  reduction  of  vital  phenomena  to  the  physico-chemical 
forces  of  materialistic  science  is  equivalent  to  the  negation 
of  becoming  and  change.  Furthermore,  becoming  and 
change  are  inexplicable  under  any  assumption  which  denies 
the  validity  of  the  two  before-mentioned  principles.  The 
Space-Time  Potential  constitutes  a  direct  challenge  to 
materialism. 

In  this  introductory  synopsis  we  shall  briefly  discuss  the 
fundamental  hypothesis  of  science  in  order  to  prove  the 
correctness  of  the  contentions  already  enunciated. 

4.    The  Unknowns  of  Science. 

The  Fundamental  Concepts  of  Materialistic  Science 

In  order  to  build  a  harmonious  logical  structure,  modern 
science  finds  it  necessary  to  invent  terms  expressive  of 
certain  phases  of  physical  phenomena.  Consequently  we 
find  in  treatises  upon  particular  branches  of  science,  such 
terms  as  "the  charge  carried  by  an  ion  or  electron,  tubes 
of  force,  electrical  field,  ether,  force,  energy,  matter,  cen- 
tral force,  attraction,  repulsion,  pressure,  temperature, 
acceleration,  velocity,  momentum,  mass,  density,  etc.,  etc." 
These  terms  of  science  may  be  broadly  divided  into  two 
classes:  those  which  pertain  to  phenomenal  phases  which 
are  directly  observed  by  the  senses ;  and  those  which  refer 
to  phases  which  are  inferred  to  exist  either  as  physical  ante- 
cedents or  causal  factors  in  the  network  of  phenomena. 

An  inferential  concept  created  by  science  for  the  pur- 
pose of  rationalizing  the  observed  facts  of  phenomena  is  of 


18  SCIENTIFIC  THEISM 

the  nature  of  an  unknown  physico-mathematical  X.  The 
scientist  may  assume  one  of  two  attitudes  toward  these 
physico-mathematical  unknowns  in  his  phenomenal  equa- 
tion ;  first,  he  may  maintain  that  such  unknowns  are  merely 
necessary  conveniences  introduced  in  order  to  complete  the 
phenomenal  equation  without  claiming  actual  reality  for 
them;  second,  he  may  claim  genuine  reality  for  these 
thought  creations  in  order  to  vitalize  and  actualize  the 
observed  phenomenal  experience.  If  the  scientist  takes  the 
second  position  he  becomes  a  philosopher  and  a  meta- 
physician. He  may  deny  this  assertion,  but  it  is  neverthe- 
less true.  Generally  the  scientist  who  aligns  himself  with 
the  second  attitude  is  a  total  failure  as  a  philosopher  and 
metaphysician,  either  because  he  is  not  in  sympathy  with 
the  philosophical  attitude,  or  because  his  lack  of  philo- 
sophical training  prohibits  him  from  developing  a  con- 
sistent, rational  system.  In  either  case  such  a  scientist  is 
profuse  in  his  denunciations  of  that  which  savors  of  meta- 
physics, even  if  he  himself  is  responsible  for  the  un- 
scientific creation.  In  order  to  avoid  the  pitfalls  of 
the  second  attitude  a  great  number  of  scientists  seek 
refuge  in  the  first  position.  This  class  of  scientists  create 
unknowns  with  impunity  because  they  do  not  feel  the 
restraint  of  responsibility  for  their  creations.  Making  no 
claims  for  the  reality  of  their  concepts,  they  feel  no  lia- 
bility in  regard  to  the  content  injected  into  them.  Phy- 
sico-mathematical conveniences  are  regarded,  by  this  scien- 
tific school,  as  having  a  right  to  exist  on  the  principle  that 
the  end  is  justified  by  the  means.  In  so  far  as  such  instru- 
ments of  convenience  deal  with  the  genuine  realities  of  a 
physical  world  they  have  no  independent,  unquestionable 
birthright,  consequently  we  may  justly  demand  that  they 
be  consistently  defined  and  definitely  related  to  that  world 
order  whose  explanation  is  their  only  reason  for  existing. 
It  is  held  that  science  finds  its  only  legitimate  and  consistent 
field  in  the  recording  and  correlation  of  experimental  facts. 
The  recording  and  correlating  of  these  facts  finally  takes 
the  form  of  some  mathematical  expression  involving  both 
types  of  factors,  the  observed  and  the  inferred.  This  is 
particularly  unfortunate  for  those  who  desire  to  avoid  de- 
fining, interpreting,  and  relating  the  inferred  factors  to  a 


SCIENTIFIC  THEISM  19 

real  world.  This  class  of  scientists  attempt  to  avoid  account- 
ability for  such  "convenience  unknowns"  by  saying  that 
they  care  not  what  they  are,  but  what  they  do. 

5.     Scientific  Concepts  Defined. 

In  order  to  examine  the  significance  and  implications  of 
the  concepts  of  modern  materialistic  science  we  shall  briefly 
define  them. 

1.  Mass  is  the  Quantity  of  Matter. 

2.  Velocity  is  distance  traversed  in  a  Unit  of  Time. 
Involves  both  Space  and  Time. 

3.  Acceleration  is  the  increase  or  decrease  in  Velocity. 
Involves  both  Space  and  Time. 

4.  Force  is,  or  is  measured  by,  Mass  multiplied  by  Accel- 
eration.   Involves  Space,  Time,  and  Mass. 

5.  Kinetic  Reaction  is,  or  is  measured  by,  Mass  multi- 
plied by  Acceleration.    Involves  Space,  Time,  and  Mass. 

6.  Impulse  is,  or  is  measured  by,  Force  multiplied  by 
Time.    Involves  Space,  Time,  and  Mass. 

7.  Work  is,  or  is  measured  by,  Force  multiplied  by  Dis- 
tance.   Involves  Space,  Time,  and  Mass. 

8.  Energy  is,  or  is  measured  by,  the  Capacity  for  doing 
Work,  or  it  is  the  Stored  Capacity  to  overcome  Force 
through  Distance.    Involves  Space,  Time  and  Mass. 

9.  Ether  is  Matter  to  Zero,  or  Infinite  Limits  including 
the  ordinary  Force  functions  correlated  with  Matter.    It  is 
Super-Matter  and  Force.    Involves  Space,  Time,  and  Mass. 

In  order  to  define  "Quantity  of  Matter"  the  materialistic 
scientist  introduces  the  term  Mass.  When  he  is  called  upon 
to  define  "Mass,"  he  states  that : 

Mass  is,  or  is  measured  by,  Force  divided  by  Accelera- 
tion ;  or  Mass  is,  or  is  measured  by,  Kinetic  Reaction  divided 
by  Acceleration. 

In  the  fourth  item  he  has  defined  Force  as  being  Mass 
multiplied  by  Acceleration,  and  in  the  fifth  item  he  has 
defined  Kinetic  Reaction  as  being  Mass  multiplied  by  Accel- 
eration. Consequently,  "Quantity,  of  Matter"  has-  been 
defined  in  terms  of  Force  and  Acceleration,  or  Kinetic  Reac- 
tion and  Acceleration.  Now  since  Force  and  Kinetic  Re- 
action have  been  defined  in  terms  of  "Quantity  of  Matter," 
Mass,  and  Acceleration,  it  follows  that  the  circle  here  com- 


20  SCIENTIFIC  THEISM 

pletes  itself,  and  therefore  it  is  clearly  evident  that  the 
materialistic  scientist  has  defined  neither  "Quantity  of  Mat- 
ter" (Mass)  nor  Force  and  Kinetic  Reaction. 

6.  The  Closed  Chain  of  Concepts. 

It  follows  from  the  above  definitions  that  the  material- 
istic scientist  has  failed  to  define  the  concepts,  Impulse, 
Work,  and  Energy,  for  the  reason  that  he  has  not  given  us 
a  satisfactory  definition  of  Force.  Hence  Impulse,  Work, 
and  Energy  are  included  in  the  closed  circle  of  his  specu- 
lations. Of  the  nine  items  considered  there  remain  the 
terms  Velocity,  Acceleration,  and  Ether.  The  last  term  will 
be  disposed  of  later  in  our  discussion.  Both  Velocity  and 
Acceleration  involve  the  notions  of  Space  and  Time.  In 
fact,  all  the  concepts  owe  whatever  significance  they  may 
possess  to  the  meaning  of  Space,  Time,  and  Mass.  We  have 
seen  that  Mass  is  in  the  closed  chain  including  Force, 
Kinetic  Reaction,  and  Acceleration. 

7.  The  Empirical  Position  of  Science. 

Is  it  pertinent  for  us  to  ask  the  materialistic  scientist 
to  define  Gpace  and  Time?  By  his  own  definitions  he  has 
been  driven  back  to  the  notions  of  Space  and  Time  as  funda- 
mentals. His  own  definitions  have  defined  nothing  because 
he  has  been  caught  in  a  circle  which  he  has  not  been  able 
to  cut.  He  has  forged  a  closed  chain  of  interdependent  con- 
ceptual links  without  being  able  to  enlighten  us  in  regard 
to  the  independent  significance  and  meaning  of  a  single 
link.  In  regard  to  the  notions  of  Space  and  Time  the  physi- 
cist may  reply  that  the  yardstick  and  the  chronometer  satis- 
factorily represent  space  and  time  for  him.  He  is  not 
interested  in  any  metaphysical  speculations  concerning  the 
ultimate  nature  of  space  and  time.  In  that  case  the  physi- 
cist becomes  an  empiricist  who  deals  only  with  experimental 
data.  As  an  empiricist  he  will  be  well  within  his  rights 
if  he  formulates  working  hypotheses  to  assist  him  in  the 
further  pursuit  of  physical  data. 

8.  Faith  in  the  Rationality  of  the  World. 

If  he  claims  any  further  significance  for  his  working 
hypotheses,  then  he  must  show  that  they  are  in  complete 
agreement  with  the  fullest  significance  of  reality.  An 


SCIENTIFIC  THEISM  21 

attempt  to  do  this-  will  take  him  beyond  the  bounds  of  em- 
pirical science,  forcing  him  into  the  field  of  "metaphysical 
speculation."  We  have  the  right  to  demand  that  his  working 
hypotheses  be  consistent  and  true  to  reality.  Moreover, 
any  hypothesis  which  purports  to  introduce  a  real  activity 
principle  into  the  universe  must  be  defined,  not  by  an  argu- 
ment in  a  circle,  but  by  a  distinct  idea  harmonious  with  the 
totality  of  the  universe.  If  it  is  his  desire  to  build  a  genuine 
dynamic  world  of  becoming  and  change,  then  his  concepts 
must  partake  of  a  basic  concept  capable  of  accounting  for 
the  real  activity  manifest  in  the  cosmos.  This  basic  concept 
must  potentially  include  all  the  observed  functions  in  the 
physical  world.  This  fundamental  concept  must  include 
reason,  purpose,  and  teleology.  Without  purpose  and  tele- 
ology, the  world  becomes  irrational.  Ultimately  our 
thoughts  and  actions  rest  upon  faith  in  the  persistence  of 
a  rational  world  order.  Moreover,  every  inference  and 
deduction  arrived  at  through  the  process  of  thought  is 
based  upon  the  fundamental  premise  that  the  world  is 
rational.  This  premise  cannot  be  derived  through  the 
method  of  logic.  Lack  of  faith  in  this  as  the  fundamentally 
given  makes  knowledge  impossible  and  transforms  cosmos 
into  chaos  through  an  absolute  skepticism.  Such  a  skepti- 
cism is  self-destructive  because  it  is  based  upon  the  self- 
annihilatory  assertion  that  the  only  truth  in  the  world  is 
that  there  is  no  truth. 

9.    The  Activity  Principle. 

The  mechanistic  models  evolved  by  the  materialistic 
scientists  are  based  upon  the  concepts  enumerated  above. 
Since  they  constitute  a  closed  chain,  their  actuating  dynamic 
principle  must  be  found  either  within  or  without  the  closed 
chain.  It  should  be  evident  that  no  genuine  and  real  ac- 
tivity principle  is  found  within  this  closed  chain.  Neither 
Force  nor  Energy  can  constitute  this  activity  principle,  be- 
cause the  former  is  defined  in  terms  of  Mass  and  Acceleration 
and  the  latter  is  measured  in  terms  of  Force  and  Distance. 

This  activity  principle  cannot  be  defined  in  terms  of 
Mass,  because  Mass  is  defined  in  terms  of  Force  and  Accel- 
eration. Underlying  the  notion  of  Acceleration  we  find  the 
basic  notions  of  Space  and  Time.  In  view  of  the  preceding, 


22  SCIENTIFIC  THEISM 

the  significance  of  the  title  "Space-Time  Potential"  should 
be  apparent. 

It  may  be  affirmed  that  in  the  synthesis  of  the  concepts 
of  either  Mass  and  Force,  or  Mass  and  Energy,  the  sought 
activity  principle  may  be  found.  The  mere  putting  together 
of  two  concepts,  neither  of  which  contains  a  third  necessary 
concept,  is  a  totally  ineffective  procedure.  Nothing  can 
come  out  of  this  mere  synthesis  other  than  that  which  is 
previously  contained  in  the  constituents.  Furthermore,  if 
the  three  concepts,  Mass,  Force,  and  Energy,  are  to  be  given 
genuine  independent  significance,  at  least  one  of  the  con- 
cepts must  be  independently  defined.  As  defined  by  science 
they  are  interdependent  and  relative,  and  as  such  have 
naught  but  relative  significance.  Speculatively,  however, 
science  thinks  of  Mass  and  Force  as  separate  and  distinct 
entities  totally  different  in  their  ultimate  nature.  This  is 
another  glaring  inconsistency  in  the  annals  of  materialistic 
science.  The  convincing  "forcefulness"  of  the  word  Force 
has  a  seductive  effect  upon  the  reasoning  faculties.  Through 
centuries  of  scientific  repetition  this  word  Force  has 
bewitched  the  reason.  It  is  the  great  ignis  fatuus  of  science 
which  lightens  the  dreary  quagmires  of  materialism. 
Within  the  closed  chain  of  scientific  concepts  we  find  noth- 
ing capable  of  generating  an  activity  principle.  In  their 
totality  these  materialistic  concepts  cannot  generate  one 
single  physical  action.  The  unbiased  thinker  is  forced  to 
the  conclusion  that  the  closed  chain  is  impotent  and 
incapable  of  evolving  a  mechanistic  model  which  can  pulsate 
with  genuine  action.  The  inference  is  forced  upon  us  that 
the  actuating  dynamic  principle  must  be  sought  outside  of 
the  closed  chain  in  the  Life  of  God.  The  immanence  of  God 
in  the  world  then  follows  as  the  only  hypothesis  which  will 
account  for  cosmic  activity. 

10.    The  Gods  of  Science. 

We  have  been  taught  to  bow  in  reverence  before  the 
shrine  of  materialistic  science  and  to  worship  its  physico- 
mathematical  gods,  and  we  are  expected  by  materialism  to 
revere  no  other  God,  for  there  is  no  God  other  than  those 
manufactured  in  the  laboratories  of  materialistic  science. 
Stripped  of  their  technical  adornment,  these  gods  of  science 


SCIENTIFIC  THEISM  23 

prove  to  be  nothing  more  than  inert  clay  energized  from 
time  to  time  by  hypodermic  injections  of  powerful  doses  of 
the  calculus.  Science  has  accomplished  wonders  through 
experimental  research,  but  when  materialism  tries  to  con- 
struct a  consistent  cosmos  from  materialistic  concepts,  then 
reason  receives  its  greatest  insult.  The  materialistic  scien- 
tist is  a  total  failure  when  he  tries  to  enter  fields  beyond 
the  confines  of  his  laboratories.  We  are  tempted  to  make 
the  sweeping  assertion  that  most  scientists  are  incapable 
of  consistent  thought  when  dealing  with  the  problems  of 
reality.  We  have  exposed  the  weakness  in  the  very  founda- 
tion of  materialism.  Even  the  least  initiated  layman  in 
science  must  revolt  at  the  thought  of  giving  reverence  to 
the  impotent  Closed  Chain  of  Concepts  manufactured  in 
the  laboratories  of  materialism.  This  closed  chain  of 
science  has  no  peer  in  the  archives  of  fallacy.  The  House 
of  Materialism  is  built  upon  a  conceptual  substructure  com- 
posed of  the  most  blatant  fallacies  ever  inflicted  upon  an 
unsuspecting  public.  The  forging  of  the  closed  chain  by 
the  blacksmiths  of  materialism  is  the  greatest  crime  ever 
committed  against  reason. 

In  the  above  we  have  shown  that  the  fundamental  con- 
cepts of  materialistic  science  have  no  significance  when 
applied  to  reality.  They  contain  no  real  actuating  prin- 
ciple as  their  common  basic  element.  Consequently,  the 
world  built  up  by  materialism  is  incapable  of  exhibiting 
phenomenal  activity.  We  have  admitted  that  empirical 
science  has  accomplished  marvels,  and  has  been  a  power  in 
the  uplift  of  mankind.  We  have  conceded  that  for  science 
the  working  hypothesis  is  indispensable.  We  have  cau- 
tioned science  not  to  claim  too  much  for  its  working 
hypotheses.  They  must  be  consistent  with  facts.  We 
demand  that  science  cease  its  scoffing  at  religion  and  phi- 
losophy because  of  its  total  failure  to  deal  consistently  with 
problems  outside  of  its  own  domain.  We  insist  that  religion 
and  philosophy  be  restored  to  their  rightful  place  in  the 
domain  of  human  affirmation  and  knowledge. 

11.    The  Blunder  of  Materialism. 

In  the  preceding  discussion  we  have  shown  that  the 
House  of  Materialism  is  built  upon  the  quicksand  of  a  Closed 


24  SCIENTIFIC  THEISM 

Chain  of  Concepts.  Not  one  conceptual  link  in  the  chain 
is  independently  defined.  Taken  in  toto  they  contain  no 
real  activity  principle  capable  of  explaining  the  smallest 
fragment  of  physical  action.  This  colossal  blunder  of  mate- 
rialism forces  us  to  look  with  suspicion  upon  its  claims  to 
superhuman  intellectual  sagacity.  The  speculative  sub- 
structure of  materialistic  science  is  devoid  of  common 
sense.  It  is  not  flattering  to  the  intellectualism  of  the  pres- 
ent century  to  be  forced  to  admit  that  a  large  percentage  of 
sincere  thinkers  have  been  completely  hoodwinked  by  the 
impotent  barrage  of  intricate  mathematics  sprayed  over  the 
battlefield  of  materialism's  Armageddon. 

Some  Auxiliary  Concepts  of  Materialistic  Science 

12.     Lines  of  Force. 

In  this  paragraph  we  shall  put  some  of  the  much  cher- 
ished auxiliary  concepts  of  materialistic  science  to  the  test  of 
common  sense.  We  shall  begin  the  investigation  by  a  con- 
sideration of  the  Tube  of  Force  developed  by  the  eminent 
English  physicist  Sir  J.  J.  Thomson,  Professor  of  Experi- 
mental Physics  in  the  University  of  Cambridge.  A  few 
citations  from  Thomson's  "Electricity  and  Matter"  will 
bring  the  notion  before  us.  "If  iron  filings  are  scattered  on 
a  smooth  surface  near  a  magnet  they  arrange  themselves 
in  well-marked  lines  which  can  be  traced  from  one  pole  of 
the  magnet  to  the  other ;  the  direction  of  these  lines  at  any 
point  coincides  with  the  direction  of  the  magnetic  forces, 
while  the  intensity  of  the  force  is  indicated  by  the  concen- 
tration of  the  lines.  ...  I  have  spoken  so  far  only  of 
lines  of  magnetic  force ;  the  same  considerations  will  apply 
to  the  electric  field,  and  we  may  regard  the  electric  field  as 
full  of  lines  of  force,  which  start  from  positively  and  end  on 
negatively  electrified  bodies.  ...  To  Faraday  the  lines 
of  force  were  far  more  than  mathematical  abstractions — 
they  were  physical  realities.  Faraday  materialized  the 
lines  of  force  and  endowed  them  with  physical  properties 
so  as  to  explain  the  phenomena  of  the  electric  field.  Thus  he 
supposed  that  they  were  in  a  state  of  tension,  and  that  they 
repelled  each  other.  Instead  of  an  intangible  action  at  a 
distance  between  two  electrified  bodies,  Faraday  regarded 


SCIENTIFIC  THEISM  25 

the  whole  space  between  the  bodies  as  full  of  stretched, 
mutually  repellent  springs.  The  charges  of  electricity  were, 
in  this  view,  just  the  ends  of  these  springs.  An  electric 
charge  was  an  extensive  arsenal  of  springs  spreading  out 
in  all  directions  to  all  parts  of  the  field.  ...  If  through 
the  boundary  of  any  small  closed  curve  in  the  electric  field 
we  draw  lines  of  force,  these  lines  will  form  a  tubular  sur- 
face, and  if  we  follow  the  lines  back  to  the  positively  elec- 
trified surface  from  which  they  start  and  forward  on  to  the 
negatively  electrified  surface  on  which  they  end,  we  can 
prove  that  the  positive  charge  enclosed  by  the  tube  at  its 
origin  is  equal  to  the  negative  charge  enclosed  by  it  at 
its  end."1 

13.    Tubes  of  Force. 

Tubes  constructed  from  lines  of  force  constitute  the 
Tubes  of  Force  of  Thomson.  He  gave  the  name  "Faraday 
Tube"  to  a  tube  of  force  which  enclosed  a  unit  charge.  He 
states  that  "motion  of  the  Faraday  tubes  is  accompanied 
by  the  production  of  magnetic  force."2  In  his  "Notes  on 
Recent  Researches  in  Electricity  and  Magnetism,"  Thomson 
states :  "The  result  of  the  different  effects  on  the  energy  of 
the  atom  produced  by  the  incidence  of  a  Faraday  Tube  will 
be  the  same  as  if  the  atoms  of  different  substances  attracted 
electricity  with  different  degrees  of  intensity.  .  .  .  The 
Faraday  tubes  when  they  reach  a  conductor  shrink  to 
molecular  dimensions."3 

The  reader  is  here  advised  to  draw  a  long  breath  for  the 
sake  of  his  health,  and  in  recognition  of  the  seeming  pro- 
fundity of  the  Thomsonian  speculations.  Let  us  examine 
the  Thomsonian  pretensions  to  profundity. 

When  iron  filings  "arrange  themselves  in  well-marked 
lines"  are  these  lines  physical  realities  or  are  they  merely 
lines  along  which  physical  realities  arrange  themselves? 
Faraday  maintained  that  the  lines  of  force  were  physical 
realities  in  order  to  avoid  the  Supreme  Terror  of  Material- 
ism, which  is  Action  at  a  Distance.  This  bogy  of  material- 


1  Electricity  and  Matter,  pp.  8,  9,  10,  14. 

1  Ibid.,  p.  18. 

8  Recent  Researches  in  Electricity  and  Magnetism,  p.  5. 


26  SCIENTIFIC  THEISM 

ism  has  always  haunted  the  scientist  and  driven  him  to 
invent  mathematical  sticks  with  which  to  bridge  the  vacuous 
abysses  between  material  particles.  The  Thomsonian  Tube 
and  the  Ether  are  mathematical  sticks  manufactured  for 
the  purpose  of  beating  the  bogy  into  insensibility.  For  the 
"simple-minded"  believer  in  God  this  bogy  has  no  terror. 
Mathematical  sticks  are  mere  worthless  playthings  vener- 
ated by  materialism.  •  In  the  following  we  shall  show  that 
with  a  proper  understanding  of  the  nature  of  Space  and 
Time  in  their  relation  to  the  Finite  and  the  Infinite,  Action 
at  a  Distance  need  cause  us  no  consternation.  Faraday's 
claim  of  physical  reality  for  the  line  of  force  involves  Thom- 
son in  the  same  contention  for  his  tube  of  force  unless  he 
repudiates  the  Faraday  interpretation.  Thomson  speaks 
about  "effect  produced  by  the  incidence  of  a  Faraday  Tube." 
He  also  refers  to  the  "motion  of  the  Faraday  tubes."  These 
statements  would  indicate  that  Thomson  believes  in  the 
physical  reality  of  his  tubes.  The  incidence  of  a  tube  could 
produce  no  effect  on  anything  unless  it  possessed  physical 
reality.  The  tube  may  be  a  thought,  a  metaphysical  concoc- 
tion, a  ghost,  a  mathematical  essence  or  extract,  an  emotion, 
a  superstition,  or  any  thingless  something,  in  which  event 
the  materialistic  scientist  would  frown  with  horror  at  the 
notion  that  such  a  "nothing"  could  do  something  and  pro- 
duce effects.  Thomson  may  reply  that  a  tube  of  force  is 
composed  of  lines  of  force  and  therefore  the  tube  is  very 
"forceful"  and  can  accomplish  almost  everything, 

14.     Force  is  not  an  Entity. 

What,  then,  of  the  line  of  force  ?  Is  it  a  mere  line  or  is 
it  force  ?  If  it  is  force,  then  we  ask  Thomson  what  he  means 
by  the  effects  produced  by  the  incidence  of  force  on  the 
atom?  Is  force  an  entity  distinct  from  matter?  If  so, 
then  we  must  assume  that  force  is  of  an  immaterial  nature. 
Materialistic  science  does  not  admit  that  the  immaterial  can 
produce  effects  upon  the  material.  Materialism  holds  that 
all  physical  change  is  brought  about  by  the  action  of  one  or 
more  material  groups  upon  another  material  group.  Science 
defines  force  in  terms  of  the  product  of  mass  and  accelera- 
tion. If  force  is  not  immaterial  and  an  entity  independent 
of  and  distinct  from  matter,  then  this  definition  conveys  no 


SCIENTIFIC  THEISM  27 

more  information  than  the  fatuous  statement  that  the 
amount  of  change  in  a  matter  group  is  proportional  to  the 
product  of  its  mass  by  the  resulting  observed  acceleration. 
In  other  words,  if  we  compare  the  product  of  mass  and 
acceleration  in  one  matter  group  with  a  similar  product  for 
a  second  matter  group  and  find  the  latter  to  be  twice  the 
former,  then  the  inference  is  that  the  amount  of  the  change 
sustained  by  the  latter  is  twice  that  of  the  former.  No  sane 
person  can  regard  this  inference  as  indicating  exceptional 
intellectual  acumen.  If  this  is  the  intent  of  the  definition 
of  force  submitted  to  us  by  science,  then  we  have  merely 
been  shown  how  to  measure  the  amount  of  the  change 
observed  in  a  matter  group.  What  is  the  reason,  then,  for 
the  feverish  desire  of  science  repeatedly  to  flaunt  the  word 
"force"  before  our  eyes  ?  If  the  latter  notion  be  the  scien- 
tific intent  of  the  word  "force,"  then  the  term  is  superfluous. 
Mass  and  acceleration  are  sufficient  for  the  purpose  indi- 
cated. The  word  "force,"  however,  has  always  contained  a 
peculiar  mystical  charm  for  science,  and  it  has  been  exceed- 
ingly useful  in  covering  a  multitude  of  sins.  Unfortunately 
for  science,  the  term  "mass"  has  been  defined  in  terms  of 
force.  Again  we  hear  the  monotonous  rattle  of  the  links 
of  the  closed  chain.  If  science  admits  that  force  is  a  genuine 
immaterial  entity  manifesting  itself  in  the  physical  uni- 
verse, then  the  House  of  Materialism  crumbles.  Material- 
ism has  then  dug  its  own  grave.  We  have  seen  that  the 
work  of  science  hinges  upon  the  validity  of  the  statement 
that  the  world  is  rational.  If  this  is  not  admitted,  then  the 
achievements  of  science  are  worthless.  Given  a  rational 
world  order  and  an  immaterial  force,  and  we  are  not  far 
distant  from  the  concept  of  God.  Through  its  own  con- 
cepts science  is  forced  to  the  concept  of  God. 

15.     The  Monon  or  Force  Center. 

We  must  not  leave  the  remarkable  tube  hypotheses  with- 
out a  reference  to  the  curious  contention  that  the  tubes  are 
in  a  "state  of  tension,  and  that  they  repel  each  other."  We 
can  conceive  of  tension  in  a  material  body,  in  which  case 
science  accounts  for  this  state  as  being  due  to  the  action 
of  a  force,  whatever  science  may  think  that  it  means  by 
force.  If  force  is  an  irrational,  immaterial  entity,  then  sci- 


28  SCIENTIFIC  THEISM 

ence  must  show  us  how  force  acts  upon  matter.  If  force  is 
matter,  then  science  faces  the  problem  of  explaining  how 
matter  acts  upon  matter.  Science  has  not  explained  either 
possibility.  If  force  is  merely  a  mathematical  term,  then 
it  is  worthless  as  a  principle  of  action.  If  force  is  a  rational 
activity  principle  manifesting  in  the  universe,  then  we  dis- 
cern the  immanence  of  God  in  the  physical  world.  A 
rational  world  order  cannot  have  been  produced  by  an  irra- 
tional entity;  hence  whatever  notion  we  hold  concerning 
force,  it  cannot  be  irrational.  No  process  of  evolution  can 
ever  generate  the  rational  from  the  irrational.  Possibly 
Thomson  wishes  us  to  think  of  his  tube  of  force  as  a  self- 
mover,  a  thing  of  primitive  and  rudimentary  life,  in  which 
event  it  would  be  able  to  produce  effects  upon  things  other 
than  itself.  If  this  be  the  Thomsonian  notion,  then  the  tube 
must  be  endowed  with  at  least  a  fragmentary  portion  of 
selective  intelligence,  otherwise  it  could  not  behave  in  a  con- 
sistent and  uniform  manner.  If  the  principle  of  selective 
intelligence  be  conceded  to  the  tube  then  the  foundations  of 
materialism  fall  and  we  are  again  brought  face  to  face  with 
the  concept  of  God.  The  tube  of  force  of  Thomson,  after 
due  consideration,  proves  to  be  a  very  hollow  concept.  The 
concept  has  merely  helped  science  to  round  out  its  complete 
fiasco  of  impotent  hypotheses.  According  to  the  view  of  the 
Space-Time  Potential,  force  and  matter  never  were  distinct 
entities.  The  definition  given  to  us  by  science  proves  this 
contention.  The  dualistic  position  of  materialism  is  a  com- 
plete failure.  We  find  the  solution  of  the  dilemma  of  mate- 
rialism in  the  variable  unity  of  force  and  matter  in  a 
genuine  Monon  or  Force  Center  which  owes  its  entire  sig- 
nificance to  the  immanent  rational  activity  of  God  in  the 
physical  universe. 

16.     The  Failure  of  Conceptual  Bridges. 

The  dualistic  theory  that  force  and  matter  are  distinct 
entities  involves  science  in  an  unending  chain  of  difficulties. 
Force  must  find  its  way  from  one  group  of  matter  to 
another;  it  must  make  itself  known  from  one  material 
aggregate  to  another  such  aggregate.  As  a  consequence  of 
these  difficulties  there  arose  the  much  mooted  question  if 
forces  can  make  themselves  known  at  a  distance  without  the 


SCIENTIFIC  THEISM  29 

intervention  of  a  transmitting  vehicle  or  medium,  or  if 
force  effects  must  have  a  medium  through  which  they  can 
travel  from  one  group  to  another.  Science  has  always 
abhorred  the  vacuum.  For  that  reason  it  created  the  notion 
of  a  medium  or  ether  to  bridge  the  gulf  between  matter 
groups.  We  shall  show  that  this  attempt  of  science  is  a 
total  failure.  All  the  sticks  and  glue  of  materialism  never 
will  bridge  the  gap.  The  concept  of  God  is  the  only  con- 
cept which  will  bridge  it.  With  this  concept,  Action  at  a 
Distance  loses  its  terrors  and  the  ether  hypothesis  becomes 
entirely  unnecessary. 

17.    The  Ether  as  a  Materialistic  Substitute  for  God. 

In  every  instance  where  materialistic  science  has  obsti- 
nately resisted  the  introduction  of  the  concept  of  God  into 
the  physical  universe  it  has  been  caught  in  a  maelstrom  of 
inconsistencies.  This  is  true  of  the  frantic  attempt  of 
materialism  to  substitute  the  concept  of  the  ether  for  the 
concept  of  God.  Materialism  has  always  looked  upon  the 
introduction  of  the  concept  of  God  into  the  physical  world 
as  the  unforgivable  sin.  The  ether  has  been  one  of  the  main 
weapons  used  by  materialism  in  its  attempt  to  drive  God 
out  of  the  universe.  If  the  world  had  not  been  completely 
etherized  into  unconsciousness  by  the  results  attained  by 
empirical  science,  then  the  ether  hypothesis  would  long  ago 
have  been  regarded  as  mere  speculation  devoid  of  logical 
consistency.  The  physical  content  of  the  ether  has  been 
determined  by  the  rigorous  method  of  mathematics.  Imag- 
ine, for  a  moment,  the  reliability  of  such  a  farcical  pro- 
cedure !  No  genuine  physical  proof  of  the  existence  of  the 
ether  has  yet  been  produced  by  science.  The  ether  is  an 
inferential  unknown  sprinkled  by  science  into  the  voids 
between  matter  particles.  What  ingredients  have  been  used 
by  science  in  the  manufacture  of  the  ether  hypothesis? 
The  calculus  plus  awe-inspiring  differential  equations  mixed 
with  as  many  inconsistencies  as  could  be  rammed  and 
tamped  into  the  confines  of  its  most  accommodating  infinite 
lack  of  limiting  boundaries.  There  are  almost  as  many 
ethers  as  there  are  physicists.  Certain  resemblances  to 
matter  are  evident  in  every  ether  hypothesis.  The  ether 
model  is  always  based  upon  certain  fundamental  properties 


30  SCIENTIFIC  THEISM 

of  matter,  reduced  either  to  zero  or  raised  to  infinite  limits. 
The  continuous  occupation  of  space  is  common  to  all  of 
them.  Matter  is  here  and  there.  Ether  is  supposed  to  be 
everywhere.  Hence  we  have,  in  the  notion,  the  space 
occupation  of  matter  raised  to  infinity.  At  the  outset 
it  was  a  protest  against  the  emission  theory  of  Newton. 
When  it  is  thought  of  as  a  solid  it  is  endowed  with 
incompressibility. 

Other  theorists  ascribe  infinite  compressibility  to  the 
ether.  F.  Neumann  and  MacCullagh  adhered  to  the  incom- 
pressibility notion,  while  Fresnel  preferred  the  hypothesis 
of  infinite  compressibility.  We  are  told  by  some  physicists 
that  the  ether  is  structureless,  incompressible,  motionless, 
but  capable  of  being  set  into  motion,  non-elastic,  capable 
of  indefinite  subdivision,  and  that  the  resulting  parts  can 
move  over  each  other  without  friction.  No  known  physical 
reality  in  the  universe  satisfies  these  specifications.  Empty 
space  (vacuum)  qualifies  better  than  any  form  of  matter. 
If  the  ether  is  not  mere  empty  void,  then  the  specifications 
are  more  closely  satisfied  by  the  supposition  that  the  ether  is 
real  but  immaterial.  Certainly  the  ether  cannot  be  material 
in  its  nature  and  satisfy  the  requirements  imposed  upon  it 
by  physical  phenomena.  After  all  is  said,  the  ether  is 
merely  an  imagined  realization  of  the  physical  requirement 
that  at  every  instant  there  shall  everywhere  be  a  reality 
which  is  in  intimate  responsive  connection  with  matter. 
This  reality  cannot  be  material  in  its  nature,  for  no  form 
or  type  of  matter  will  satisfy  its  requirements  as  outlined 
by  science.  The  writer,  in  his  Space-Time  Potential  has 
considered  all  the  phases  and  implications  of  the  ether 
hypothesis.  In  every  form  of  the  hypothesis  one  basic  ele- 
ment is  missing,  without  which  the  ether  model  becomes 
inoperative.  This  basic  element  is  selective  intelligence.  It 
is  not  to  be  inferred  that  the  addition  of  the  element  of 
selective  intelligence  will  make  the  ether  model  operative; 
on  the  contrary,  the  hypothesis  is  so  filled  with  incon- 
sistencies that  it  is  beyond  redemption.  The  absence  of  the 
element  of  selective  intelligence,  taken  in  conjunction  with 
the  fact  that  the  sought  for  reality  must  be  immaterial, 
indicates  that  we  are  again  face  to  face  with  the  concept 
of  God.  Any  possible  future  substitute  for  the  ether 


SCIENTIFIC  THEISM  31 

hypothesis  will  involve  similar  difficulties  and  inconsist- 
encies unless  the  concept  of  God  becomes  the  basic  element 
of  its  hypothetical  content.  The  concept  of  God  solves  the 
riddle  of  the  physical  universe.  All  the  concepts  of  science 
cannot  displace  it  as  the  keystone  of  the  universe.  The 
inadvertent  groping  of  materialism  for  a  substitute  for  the 
concept  of  God  has  opened  the  door  of  reality  and  brought 
to  us  the  realization  that  its  search  is  futile  unless  it  admits 
the  fundamental  truth  of  religion. 

18.    The  Contribution  of  Boscovich. 

The  problem  of  Action  at  a  Distance  has  always  been 
a  bugaboo  to  the  scientific  world.  Stated  concisely,  the 
question  is,  Can  matter  act  where  it  is  not?  Must  discrete 
portions  of  matter  be  connected  by  an  intermediate  some- 
thing, a  medium,  plenum,  or  ether,  by  means  of  which  one 
material  system  can  be  placed,  as  it  were,  en  rapport  with 
another  distant  material  system?  Daniel  Bernoulli 
answered  the  former  question  in  the  affirmative  and  denied 
the  necessity  of  a  medium.  Ruggiero  Giuseppe  Boscovich, 
the  brilliant  Jesuit  mathematician,  physicist,  and  astrono- 
mer, professor  of  mathematics  at  the  Collegium  Romanum, 
in  a  work  entitled  "Theoria  Philosophia  Naturalis,"  pub- 
lished at  Vienna  in  1758,  maintained  with  Daniel  Bernoulli 
that  action  at  a  distance  is  possible  through  an  absolute 
vacuum.  For  him  matter  consisted  merely  of  force  centers 
endowed  with  inertia,  and  all  physical  and  chemical  activi- 
ties were  explainable  as  mutual  attractions  and  repulsions 
varying  in  intensity  with  the  magnitude  of  the  intervening 
distance.  The  prophetic  vision  of  Boscovich  concerning  the 
ultimate  nature  of  matter  has  recently  been  verified  by  the 
researches  of  Kaufmann  (1903),  J.  J.  Thomson,  Heaviside, 
and  Searle.  These  famous  physicists  may  be  loath  to  admit 
that  they  have  experimentally  verified  the  contentions  of 
Boscovich  concerning  the  nature  of  matter.  In  fact,  we  sus- 
pect that  they  would  reprimand  us  in  no  uncertain  language 
if  we  insinuated  that  they  have  contributed  one  iota  to  the 
force-center  theory.  Dr.  Rutherford,  referring  to  the  work 
of  these  men  in  his  book  entitled  "Radio- Activity,"  says: 
"The  above  results  are  therefore  in  agreement  with  the  view, 
that  the  mass  of  the  electron  is  altogether  electrical  in 


32  SCIENTIFIC  THEISM 

origin  and  can  be  explained  purely  by  electricity  in  motion."1 
In  his  "Electricity  and  Matter,"  J.  J.  Thomson  states :  "I 
have  calculated  from  this  expression  the  ratio  of  the  masses 
of  the  rapidly  moving  particles  given  out  by  radium  to  the 
mass  of  the  same  particles  when  at  rest,  or  moving  slowly, 
on  the  assumption  that  the  whole  of  the  mass  is  due  to  the 
charge,  and  have  compared  these  results  with  the  values  of 
the  same  ratio  as  determined  by  the  Kaufmann  experiments. 
These  results  support  the  view  that  the  whole  mass  of  these 
electrified  particles  arises  from  their  charge."2 

19.  The  Divisibility  of  the  Atom. 

The  eternally  stable  and  unchanging  atom  of  Dalton  is 
gone  forever.  The  atom  is  composed  of  sub-atomic  parts. 
It  is  a  veritable  microcosm,  a  minute  planetary  system 
whose  constituent  parts  are  in  continuous  motion.  It  is 
composed  of  such  smaller  primordial  parts  as  electrons  or 
corpuscles  whose  mass  is  not  fixed,  but  changes  with  a 
change  in  velocity.  Science  measures  force  in  terms  of  the 
product  of  mass  and  acceleration.  In  the  electronic  particle 
we  have  a  changing  entity  whose  magnitude  is  measurable 
in  terms  of  force.  Therefore  we  assert  that  scientific  re- 
search has  brought  us  back  to  the  force  center  of  Father 
Boscovich. 

20.  Mass  and  the  Ether. 

Further  on  in  the  same  work,  Thomson  continues :  "All 
mass  is  mass  of  the  ether,  all  momentum,  momentum  of  the 
ether,  and  all  kinetic  energy,  kinetic  energy  of  the  ether. 
This  view,  it  should  be  said,  requires  the  density  of  the 
ether  to  be  immensely  greater  than  that  of  any  known  sub- 
stance."' It  is  evident  that  Thomson  is  no  intentional  sup- 
porter of  the  force  center  theory  of  Boscovich.  Again  the 
ether  becomes  the  scapegoat  for  the  farcical  speculations  of 
science.  Thomson  also  states  that  "the  whole  mass  of  any 
body  is  just  the  mass  of  ether  surrounding  the  body  which 
is  carried  along  by  the  Faraday  tubes  associated  with  the 


1  Radio-Activity ,  p.  112. 

2  Electricity  and  Matter,  pp.  47,  48,  51. 
*Ibid,  p.  51. 


SCIENTIFIC  THEISM  33 

atoms  of  the  body."1  In  speaking  of  the  constitution  of  the 
atoms,  Thomson  says :  "Let  us  then  take  as  our  primordial 
system  an  electrical  doublet,  with  a  negative  corpuscle 
(electron)  at  one  end  and  an  equal  positive  charge  at  the 
other,  the  two  ends  being  connected  by  lines  of  electric  force 
which  we  supposed  to  have  a  material  existence."3 

We  are  told  by  science  that  the  mass  (quantity  of  mat- 
ter) of  the  electron  (or  corpuscle)  is  altogether  electrical 
in  origin.  The  whole  mass  is  due  to  the  electrical  charge. 
Then  we  are  informed  that  the  whole  mass  of  any  body  is 
just  the  mass  of  ether  surrounding  the  body  which  is  car- 
ried along  in  the  moving  van  composed  of  Faraday  tubes 
associated  with  the  atoms  of  the  body.  Atoms  are  composed 
of  negative  corpuscles  and  positive  charges  hitched  together 
with  material  ropes  called  lines  of  electric  force.  The  mass 
of  any  body  is  not  the  mass  of  the  body,  but  it  is  the  mass  of 
the  ether  which  surrounds  it.  The  mass  of  your  body  is  the 
mass  of  the  clothes  which  surround  you.  Atoms  are  com- 
posed of  electrons.  Electrons  are  electrical.  Electricity  is 
mass,  and  mass  is  ether,  and  the  ether  must  be  immensely 
denser  than  a  materialist,  or  any  other  known  substance, 
in  order  to  behave  properly.  Lines  of  electric  force  are 
material.  Matter  is  electrical.  Thus  the  materialistic 
scientists  disport  themselves  on  their  conceptual  merry-go- 
round  whilst  the  calliope  of  materialism  shrieks  its  weird 
song,  "Great  is  the  Ether  of  the  Materialist!"  We  have 
disposed  of  the  ether  as  an  absurd,  fantastic  inconsistency. 

21.     Physical  Action  Involves  Action  at  a  Distance. 

Returning  to  the  problem  of  Action  at  a  Distance,  we 
have  shown  in  the  Space-Time  Potential  that  physical  action 
is  impossible  unless  we  assume  that  action  at  a  distance  is 
possible.  The  assumption  that  contact  in  space  is  the  indis- 
pensable preliminary  condition  for  mutual  action  is  of  no 
avail  because  we  must  explain  why  and  how  spatial  contact 
causes  previously  independent  and  alien  things,  states,  or 
forces  to  become  interested  in  each  other,  thus  producing 
the  phenomena  of  change.  The  fundamental  error  under- 
lying all  scientific  hypotheses  is  the  supposition  that  things 


1  Electricity  and  Matter,  p.  51. 
1  Ibid. 


34  SCIENTIFIC  THEISM 

are  independent.  If  things  are  independent,  then  action  at 
a  distance  becomes  inconceivable.  The  gap  between  inde- 
pendent things  must  be  bridged.  Consequently  science  drags 
forth  its  conceptual  sticks  and  glue  in  order  to  unite  the 
independent  things.  If  the  things  of  the  physical  universe 
are  independent,  then  all  the  conceptual  sticks  and  glue  of 
science  cannot  make  them  mutually  dependent.  Materialism 
has  struggled  to  build  a  consistent  model  of  the  physical 
universe  from  independent  things  and  scientific  concepts. 
We  have  seen  the  House  of  Materialism  crumble  because  of 
its  inconsistent  and  impotent  hypotheses.  The  failure  of 
materialism  is  complete.  We  shall  show  in  detail  in  the 
following  chapters  that  physical  action  is  impossible  unless 
we  admit  the  mutual  dependence  of  all  centers  of  reality 
in  an  interacting  unitary  system.  In  such  a  system  action 
at  a  distance  is  easily  comprehended  and  loses  all  its  repul- 
siveness.  This  interacting  unitary  system  is  the  finite  pro- 
jection of  God  in  Space  and  Time.  The  eternal  immanence 
of  God  maintains  the  system. 

22.     Summary  of  the  Criticism. 

In  the  preceding  critical  review  of  the  position  of  science 
we  have  shown : 

1.  That  such  scientific  concepts  as  mass,  force,  energy, 
and  work  are  conceptual  links  in  a  closed  chain,  out  of 
which  science  cannot  extricate  itself.    Within  this  closed 
chain  there  is  no  genuine  activity  principle  capable  of  gen- 
erating  physical   action.     The    actuating    principle    must 
therefore  be  found,  outside  of  the  closed  chain,  in  the  Life 
of  God. 

2.  That  such  auxiliary  concepts  of  science  as  tubes  of 
force  and  the  ether,  strangle  themselves  by  their  own  incon- 
sistencies.   Every  concept  of  science  can  be  shown  to  be 
merely  a  link  in  an  impotent  closed  chain.    Without  the  con- 
cept of  God  these  scientific  concepts  have  no  real  signifi- 
cance.   Many  of  the  concepts,  like  the  tube  of  force  and  the 
ether,  are  so  grossly  inconsistent  and  inconceivable  that 
they  must  be  abandoned  if  science  desires  to  retain  even  a 
vestige  of  self-respect.    Concepts  like  the  tube  of  force  and 
the  ether  are  attempts  of  materialism  to  get  along  without 
the  concept  of  God.  These  attempts  have  proved  total  fail- 


SCIENTIFIC  THEISM  35 

ures.  In  trying  to  bridge  the  voids  between  matter  groups 
by  ethers  and  similar  fantastic  and  irrational  concoctions, 
science,  by  its  own  blunders,  has  led  us  face  to  face  with  the 
concept  of  God. 

3.  That  the  horror  of  materialism  for  the  vacuum  is  at 
the  root  of  its  obstinate  refusal  to  admit  the  possibility  of 
action  at  a  distance.    Science,  in  committing  the  error  of 
refusing  to  admit  action  at  a  distance,  implicated  itself  in 
the  more  fundamental  error  of  assuming  that  things  are 
unrelated  and  independent.    A  rational  world  order  cannot 
be  constructed  from  unrelated  independent  things.     We 
must  admit  the  mutual  dependence  of  all  centers  of  reality 
in  a  world  system  which  is  unitary  and  interacting.     If 
we  do  not  admit  this,  then  a  physical  universe  is  impossible. 
The  unitary  interacting  system,  composed  of  centers  of 
mutually  dependent  reality,  is  itself  merely  an  inoperative 
phantom  of  speculation  without  the  concept  of  God's  main- 
taining  immanence   within   the   system.    Every   physical 
action  involves  the  possibility  of  action  at  a  distance.    Mere 
spatial  contact  affords  no  means  of  accounting  for  physical 
action.    In  a  unitary  interacting  system  maintained  by  the 
immanence  of  God,  action  at  a  distance  is  easily  com- 
prehended. 

4.  That  the  experimental  method  employed  by  science  in 
its  investigation  of  physical  phenomena  has  brought  great 
blessings  to  mankind.     We  give  this  method  our  hearty 
approval.    Through  this  fruitful  and  sound  method  science 
has  inadvertently  and  unintentionally  reduced  matter  to  a 
form  of  reality  totally  different  from  its  own  cherished 
notions  of  fixedness  and  eternal  permanence.     The  atom 
has  been  shown  to  be  composed  of  sub-atomic  parts  capable 
of  mass  variation  with  changes  in  velocity.    The  resistive 
ability  of  these  sub-atomic  parts,  known  as  electrons  or 
corpuscles,  is  all  that  remains  of  their  materiality.     The 
complete  physical  measure  of  the  magnitude  of  the  electron 
must  involve  the  product  of  its  two  constituent  variables, 
that  is,  mass  and  acceleration  considered  as  two  phenomenal 
aspects  of  a  single  unity.    Science  has  given  the  name  of 
force  to  this  product.    It  is  evident  that  scientific  research 
has,  consequently,  dematerialized  matter  and  given  us  a 
center  of  reality  alien  to  matter  and  identical  with  force. 


36  SCIENTIFIC  THEISM 

The  vision  of  the  great  Jesuit  physicist,  Father  Boscovich, 
has  been  unintentionally  verified  by  the  recent  investigations 
of  science.  The  force  center  of  Boscovich  is  the  ultimate 
unit  of  physical  reality.  Boscovich  ascribed  the  property  of 
inertia  to  his  force  center.  This  inertia  of  the  Boscovichian 
force  center  corresponds  to  the  resistivity  of  the  primordial 
particle.  The  materialists  have  inadvertently  given  a  spir- 
itual significance  to  the  physical  universe.  We  cannot  con- 
ceive a  rational  universe  arising  from  an  irrational  activity 
principle.  Therefore  force  is  a  manifestation  of  a  rational 
actuating  principle  immanent  in  the  physical  universe.  Con- 
sequently the  concept  of  God  becomes  indispensable  to  the 
existence  of  the  physical  universe.  Thus  we  observe  that 
materialism  has  dug  its  own  grave. 

The  above  epitomized  facts,  together  with  the  deduc- 
tions therefrom,  form  the  basis  of  the  Space-Time  Potential, 
whose  salient  features  will  now  be  considered. 

23.    Fundamentals  of  the  Space-Time  Potential. 

The  basic  principles  of  the  Space-Time  Potential  are : 

1.  The  existence  of  God. 

2.  All  reality  owes  its  existence  and  maintenance  to  God. 

3.  The  immanence  of  God  throughout  the  universe,  and 
also  His  transcendence. 

4.  The  cosmos  is  a  unitary,  interacting,  rational,  pur-    Q  ^ 
posive,  and  teleological  system.     It  is  a  finite  projection   /. 
of  the  Infinite. 

These  fundamental  principles,  having  been  established 
by  a  process  of  deduction  from  the  known  to  the  unknown, 
constitute  the  fundamental  truths  upon  which  our  system 
is  based.  Upon  these  basic  truths  we  can  construct  a  con- 
sistent model  of  the  universe.  If  these  truths  are  not 
granted,  a  consistent  model  cannot  be  constructed.  These 
fundamental  verities  must  be  incorporated  into  any  model 
of  the  physical  universe  if  it  is  to  be  a  true  representation 
of  a  dynamic  world  of  becoming  and  change. 

The  finite  projection  of  God,  manifest  in  space  and  time, 
may  be  subdivided  into  three  worlds:  (1)  The  World  of 
Energy,  Force,  and  Life;  (2)  The  World  of  Conscious 
Selves;  and  (3)  The  World  of  Subconsciousness.  The 
Space-Time  Potential  deals  only  with  the  physical  universe, 


SCIENTIFIC  THEISM  37 

and  hence  its  problem  is  the  interpretation  of  the  manifes- 
tation of  God  as  the  ultimate  source  of  the  Potential  charted 
in  Space  and  Time. 

When  we  speak,  in  the  third  basic  truth,  of  the  imma- 
nence of  God,  we  do  not  think  of  God  as  a  machinist  stroll- 
ing about  the  universe  with  an  ever-ready  oil  cup  with  which 
to  oil  the  creaking  bearings  of  the  cosmic  machinery.  On 
the  contrary,  we  think  of  the  universe  as  a  completed  finite 
projection,  capable  of  exhibiting  through  secondary  causes 
those  uniformities  which  we  call  natural  laws,  yet  incapable 
of  continuous  existence  in  space  and  time  without  the  con- 
tinuous sustaining  potential  of  God's  unceasing  existence. 
By  "immanence"  we  mean  the  continuous  dependence  of 
the  cosmos  upon  the  Being  of  God.  We  also  use  the  word 
"immanence"  to  convey  the  thought  that  God's  interest  in 
His  create  universe  is  continuous  and  does  not  cease  with 
the  act  of  create  projection.  The  dependence  of  the  phy- 
sical universe  upon  the  maintaining  activity  of  God  is  some- 
what analogous  to  the  steady  flow  of  water  in  pipes  due  to 
the  maintenance  of  an  uninterrupted  pressure-head.  Remove 
the  pressure-head  and  the  water  ceases  to  flow.  Similarly, 
in  the  case  of  the  flow  of  electricity,  this  phenomenon 
depends  upon  the  continuous  maintenance  of  a  difference  of 
electric  potential. 

24.    The  Existence  of  God  Proved  from  the  Facts  of  Science. 
Physical  Proof  of  the  Existence  of  God. 

The  Space-Time  Potential  involves  a  physical  proof  of 
the  existence  of  God.  Science  defines  the  potential  energy 
of  a  body  as  being  equal  to  the  work  required  to  bring  the 
body  from  that  position  in  which  its  potential  is  equal  to 
zero  to  the  point  of  known  potential.  Consequently  the 
potential  at  any  point  is  equal  to  the  work  done  in  bringing 
a  unit  mass  from  an  infinite  distance  to  that  point.  Now  to 
bring  a  body  or  particle  through  an  infinite  distance  requires 
an  infinite  time;  therefore  this  hypothetical  body  has  not 
yet  arrived  at  its  destination,  and  it  can  never  arrive  within 
the  confines  of  this  physical  universe.  To  regard  the  uni- 
verse as  infinite  merely  makes  the  problem  more  impossible. 
Hence,  whether  we  regard  the  physical  universe  as  finite  or 


38  SCIENTIFIC  THEISM 

infinite  in  no  way  changes  or  affects  the  conclusion.  It  may 
be  contended  that  this  argument  is  worthless  if  it  be 
assumed  that  the  primordial  elements  have  always  existed 
and  that  for  the  elementals  of  the  universe  there  is  neither 
a  time  of  beginning  nor  a  time  of  ending.  This  contention 
in  no  way  affects  our  conclusion,  for  the  reason  that  what- 
ever potential  a  particle  may  possess  at  any  given  point  in 
space  at  any  particular  moment  in  time,  this  potential  is 
equal  to  that  which  would  have  been  produced  if  the  particle 
had  previously  traversed  an  infinite  distance  in  order  to 
arrive  at  the  given  point.  Now  an  infinite  distance  or  time  is 
not  a  completed  something.  The  term  "infinite"  means 
nothing  at  all  unless  it  refers  to  some  type  of  process  which 
cannot  be  completed.  For  this  reason  the  appeal  to  an 
infinite  time  is  futile.  It  follows  that  the  observed  potential 
of  an  actual  particle  or  body  existing  in  the  physical  uni- 
verse may  be  attributed  to  the  following  sources: 

1.  To  a  motion  of  the  particle  through  an  infinite  dis- 
tance. 

2.  To  an  actuating  and  energizing  agency  within  the 
system  of  the  physical  universe. 

3.  To  an  actuating  and  energizing  agency  without  the 
physical  universe. 

We  shall  consider  these  possible  assumptions  in  the 
order  given. 

1.  We  have  shown  that  the  first  supposition  is  impos- 
sible because  a  motion  through  an  infinite  distance  involves 
motion  which  cannot  be  completed  in  either  finite  or  infinite 
time.    Infinite  distance  or  infinite  time  means  that  which 
cannot  be  completed.    If  it  does  not  mean  this,  it  has  no 
meaning  at  all. 

2.  The  injection  of  the  idea  that  the  particle  is  located 
an  infinite  distance  from  some  given  point  is  resorted  to 
for  the  purpose  of  giving  the  particle  a  zero  energy  or 
potential  value.    The  procedure  therefore  involves  the  fur- 
ther assumption  that  the  potential  energy  of  the  particle  has 
changed  from  zero  potential  to  a  potential  other  than  zero. 
Was  this  change  in  the  energy  of  the  particle  brought  about 
by  the  particle  itself  or  by  some  other  particle?    It  could 


SCIENTIFIC  THEISM  39 

not  have  been  brought  about  by  the  original  particle  with- 
out ascribing  to  that  particle  the  possibility  of  originating 
something  out  of  nothing,  in  which  case  the  result  would 
be  due  to  a  genuine  creative  act,  and  the  particle  must,  in 
that  event,  possess  an  attribute  which  we  ascribe  only  to 
God,  the  Creator  of  all  things.  If  we  maintain  that  the 
potential  of  the  given  particle  is  due  to  the  actual  potential 
of  one  or  more  other  particles,  then  we  demand  that  the 
source  of  their  potential  be  shown.  An  attempt  to  evolve 
the  potential  of  these  other  particles  involves  the  same  fruit- 
less procedure  as  for  the  given  particle.  The  search 
through  the  universe  for  a  particle  or  particles  which  can 
supply  us  with  this  initial  source  of  potential  is  conse- 
quently futile.  Therefore  no  particle  exists  within  the  phy- 
sical universe  which  can  supply  us  with  the  initial  source 
of  energy. 

3.  It  follows  that  the  observed  potential  of  any  particle 
or  body  existing  in  the  physical  universe  is  due  to  an  actuat- 
ing, energizing  principle  other  than  the  mere  physical  con- 
stituents or  force  functions  extant  within  the  physical  uni- 
verse. Again  we  are  forced  to  the  conclusion  that  God, 
and  God  alone,  is  the  source  of  the  difference  in  potential 
existing  in  the  physical  universe  as  manifest  in  the  Space- 
Time  Potential.  The  dynamics  of  the  physical  universe, 
that  is,  the  ability  of  particles  to  interact,  depends  upon 
the  continuous  maintenance  of  a  difference  of  potential 
through  the  activity  of  God.  This  conclusion  does  not 
involve  God  in  individual  activities  from  particle  to  particle 
ad  infinitum,  but  it  does  mean  that  the  final  potential  differ- 
ence ultimately  reached  is  maintained  by  the  activity  of 
God.  The  universe  is  otherwise  a  complete  uniformity 
within  itself.  We  have  therefore  proved  the  existence  of 
God  by  using  the  facts  of  physical  science.  Our  reasoning 
is  like  that  of  St.  Paul  the  Apostle,  in  his  Epistle  to  the 
Romans,  Chapter  I,  verse  20 :  "For  the  invisible  things  of 
Him  from  the  creation  of  the  world  are  clearly  seen,  being 
understood  by  the  things  that  are  made,  even  His  eternal 
power  and  Godhead ;  so  that  they  are  without  excuse."  The 
existence  of  God  has  been  proved  by  reasoning  from  the 
known  phenomena  of  the  physical  universe.  Without  a 
difference  of  potential,  physical  action  of  any  kind  what- 


40  SCIENTIFIC  THEISM 

soever  is  impossible.  We  have  shown  that  from  this  fact 
it  follows  that  the  physical  universe  is  impossible  without 
the  concept  of  God,  and  materialism  has  been  shown  to  be 
the  greatest  fallacy  of  the  ages. 

The  justification  for  the  use  of  the  word  "potential"  in 
our  title  is  now  apparent.  The  significance  of  the  "Space- 
Time"  in  the  title  will  be  evident  from  the  considerations 
which  follow.  In  the  first  article  we  defined  the  funda- 
mental concepts  of  science  and  showed  that  all  the  concepts 
are,  in  their  final  analysis,  related  to  and  dependent  upon 
the  notions  of  space  and  time.  The  term  "mass"  has  been 
reduced  to  a  force  manifestation  in  space  and  time.  The 
meaning  of  the  terms  "space"  and  "time"  is  therefore  essen- 
tial to  our  system. 


._    .    JvOrrs  • 

25.  Space  Defined. 

Space  is  a  "form  of  apprehension  or  awareness  which 
permits  the  intelligible  relations  of  bodies  to  exhibit  them- 
selves to  us  as  an  externally  ordered  arrangement.  Space, 
then,  owes  its  full  significance  not  only  to  the  perceiving 
subject,  but  also  to  the  existing  intelligible  relations  between 
things. 

26.  Time  Defined. 

Time  is  a  form  of  apprehension  or  awareness  which 
permits  the  intelligible  arrangement  of  events  to  be  pre- 
sented to  us  as  interrelated,  durational,  and  successional 
series.  Both  these  subjective  forms  depend  upon  the  intel- 
ligible coherence  of  all  that  is  real  as  that  basic  element 
which  generates  them  through  interaction  of  subject  and 
object. 

With  this  view  of  space  and  time,  action  at  a  distance 
is  readily  granted.  We  have  proved  by  a  detailed  discussion 
of  the  problem  in  our  Space-Time  Potential  that  actual  phy- 
sical phenomena  are  impossible  without  the  admission  of 
the  possibility  of  action  at  a  distance. 

27.  The  Primordial  Activity  Center,  The    Monori. 

The  most  elemental  create  reality  manifest  in  the  Space- 
Time  Potential  is  the  force  center  of  Boscovich,  to  which 


SCIENTIFIC  THEISM  41 

the  writer  has  given  the  name  "monon."  The  spatial  back- 
ground is  a  chart  of  potential  energy  values  in  which  the 
kinetic  energy  centers,  the  monons,  manifest  at  definite 
positions  or  points.  The  monons,  in  addition  to  being 
energy,  are  potential  matter.  Therefore  we  assign  them 
the  fundamental  property  or  capability  of  exhibiting  resist- 
ance to  that  which  tends  JQ  give  them  acceleration ;  in  other 
words,  we  attribute  kinetic  reaction  to  them  as  their  basic 
phenomenal  property.  The  monon  is  capable  of  exhibiting 
both  a  negative  and  a  positive  phase  of  activity.  The  nega- 
tive phase  appears  as  kinetic  reaction  or  resistance.  The 
positive  phase,  due  to  its  intrinsic  content  of  kinetic  energy, 
is  manifest  as  attraction.  Both  attraction  and  repulsion  are 
included  in  the  content  of  the  monon.  Since  kinetic  reaction 
involves  a  potential  or  possible  mass  coupled  inseparably 
with  a  possible  acceleration,  we  include  these  factors  in  the 
content  of  the  monon  with  full  realization  that  mass  and 
acceleration  are  mutually  dependent  variables  capable  of  all 
the  shades  of  variability  from  a  minimum  to  a  maximum. 
Within  certain  critical  values  we  may  therefore  find  that 
the  variation  of  mass  of  the  monon  is  practically  reduced 
to  its  zero  limit;  in  other  woras,  below  this  critical  value 
the  mass  of  the  monon  may  appear  to  je  maintained  at  a 
constant  value. 

28.    The  Energon. 

The  further  development  of  our  system  requires  that 
its  kinetic  energy  be  defined,  in  part,  in  terms  of  motion, 
for  the  reason  that  all  mechanico-physical  phenomena  are 
ultimately  reduced  to  terms  of  motion.  This  involves  the 
existence  of  gyrational  groups  of  monons.  A  rotary  system 
composed  of  two  diametrically  opposite  monons  constitutes 
our  simplest  gyratory  group.  We  have  given  the  name 
"energon"  to  this  gyratory  group.  Like  the  monon,  the 
energon  must  include  both  attraction  and  repulsion  in  its 
content.  In  order  to  meet  the  requirements  of  certain  class 
phenomena  like  the  phenomenon  of  light,  we  consider  these 
phenomena  as  being  due  to  the  interaction  of  a  translatory 
system  and  a  vibratory  and  translatory  auxiliary  system.  To 
the  former  we  give  the  name  "excitant  system,'*  and  to  the 
latter  we  apply  the  term  "concurrent  system." 


42  SCIENTIFIC  THEISM 

29.  The  Excitant  and  the  Concurrent  System. 

The  simplest  physical  phases  of  interaction  are  repulsion 
and  attraction,  reaction  and  action.  These  opposed  forms 
of  physical  action  represent  the  negative  and  positive 
phases  of  all  types  of  reality  regardless  of  complexity.  The 
negative  and  positive  functions  are  not  independent  exist- 
ences ;  on  the  contrary,  both  are  manifestations  of  a  primary 
unity,  the  former  insures  the  self-preservation  and  survival 
of  the  center  of  reality,  while  the  latter  provides  for  pos- 
sible attractive  manifestations.  In  physical  action  of  a 
vibratory  order  the  differentiation  of  the  unity  of  physical 
reality  into  two  systems  of  the  excitant  and  the  concurrent 
is  in  complete  harmony  with  the  basic  facts  of  physical 
action,  which  always  involve  action  and  reaction.  Both  the 
excitant  and  the  concurrent  system  are  ultimately  com- 
posed of  the  same  kind  of  discrete  energy  group.  We  dis- 
card the  notion  of  a  continuum  or  ether,  because  of  its 
many  contradictory  and  ultra-material  concepts.  The  same 
properties  and  laws  of  action  pertain  to  both  the  excitant 
and  the  concurrent  system.  This  gives  us  a  hypothetical 
physical  basis  for  a  theory  of  relativity.  The  velocity  of 
light  becomes  the  limiting  constant  in  the  relativity  system. 
Ultra-atomic  velocities  approach  this  limit  but  do  not  reach 
it.  The  constancy  of  mass  disappears  and  its  variable 
dependence  upon  concomitant  phenomena  appears  as  a  real 
factor  in  physical  change.  In  the  mathematical  portions  of 
the  Space-Time  Potential  the  writer  has  developed  the  rela- 
tions between  mass  variation,  velocity  in  general,  and  the 
velocity  of  light.  The  results  are  in  agreement  with  the 
researches  of  Kaufmann.  The  Space-Time  Potential  is 
a  system  of  relativity. 

30.  The  Three  Phases  of  the  Energon. 

In  order  to  account  for  physical  action  we  assume  that 
the  energon  is  capable  of  change  in  a  twofold  manner  from 
its  neutral  condition.  Consequently  there  is  involved  an 
ascending  process  and  a  descending  process.  The  former 
involves  a  definite  work  increment,  the  latter  involves  an 
equal  work  decrement.  The  three  corresponding  phases  of 
the  energon  may  be  designated  as  the  high,  the  neutral,  and 


SCIENTIFIC  THEISM  43 

the  low  phase.  In  the  high  phase  the  energon  becomes  an 
electron.  In  the  low  phase  the  energon  becomes  a  "positon." 
The  word  "positon"  indicates  that  the  energon  exists  in  that 
phase  which  is  the  extreme  of  the  electronic.  The  primor- 
dial energon  constitutes  the  neutral  phase  of  the  variable 
system.  A  negative  charge  is  always  associated  with  the 
free  electron.  We  associate  an  equal  positive  charge  with 
the  positon.  In  the  last  analysis  the  magnitude  of  this 
negative  and  positive  charge  depends  upon  the  work  incre- 
ment and  its  equivalent  work  decrement.  Work  expended 
is  always  equal  and  concomitant  with  work  stored.  Ions 
in  solution  exhibit  these  three  phases  in  accordance  with 
the  precise  phase  change  in  the  energon.  Since  all  inter- 
action presupposes  the  concomitance  of  both  the  ascending 
and  descending  processes,  it  follows  that  the  products  of 
solution  must  appear  as  ionic  pairs.  In  this  we  have  a  con- 
sistent hypothetical  reason  why  molecules  break  down  into 
so-called  ionic  pairs. 

31.    The  Planetary  Orbits  from  the  Standpoint  of  the  Space- 
Time  Potential. 

One  of  the  fundamental  assumptions  of  the  Space-Time 
Potential  is  that  whatever  laws  pertain  to  the  elementals 
of  the  universe,  these  laws  pertain  also  to  their  aggregates 
irrespective  of  their  magnitude.  Consequently  the  story  of 
the  microcosm,  the  little  world  of  sub-atomic  particles, 
atoms,  and  molecules,  is  also  the  story  of  the  macrocosm, 
composed  of  those  great  aggregates  of  elementals  which  we 
know  as  planetary  and  stellar  bodies.  Therefore  any  system 
which  must  introduce  arbitrary  constants  in  passing  from 
the  microcosm  to  the  macrocosm  in  order  to  account  for 
the  gaping  discrepancies  between  the  enormous  energies 
exhibited  during  interaction  by  the  sub-atomic  particles 
and  those  shown  by  ordinary  physical  bodies,  cannot 
be  a  true  representation  of  the  physical  universe.  This 
is  the  case  with  modern  science.  This  inconsistency 
is  not  encountered  in  the  Space-Time  Potential.  The 
laws  by  which  we  interpret  the  activities  within  the 
microcosm  are  equally  applicable  to  physical  action  in 
the  macrocosm.  We  are  not  forced  to  inject  arbitrary  con- 
stants in  order  to  bridge  the  enormous  energy  differences. 


44  SCIENTIFIC  THEISM 

Our  mathematical  investigations,  based  upon  the  Space- 
Time  Potential  and  agreeing  with  the  results  of  research, 
bear  out  this  contention. 

32.     Qualities  Essential  to  the  Monon. 

We  hold  that  the  physical  universe  cannot  be  explained 
by  mere  number  alone.  Thomson  has  tried  to  build  up  the 
different  types  of  atoms  by  increasing  and  decreasing  the 
number  of  the  constituent  sub-atomic  particles  constituting 
his  model.  The  procedure  is  analogous  to  the  following : 

One  pound  of  sugar  plus  one  pound  of  sugar  equals  two 
pounds  of  sugar.  Two  pounds  of  sugar  plus  one  pound  of 
sugar  equals  three  pounds  of  salt.  Three  pounds  of  salt 
plus  one  pound  of  salt  equal  four  pounds  of  salt.  Four 
pounds  of  salt  plus  one  pound  of  salt  equal  five  pounds  of 
pepper.  In  other  words,  the  different  types  of  atoms  are 
due  to  a  difference  in  the  number  and  arrangement  of  the 
constituent  particles.  We  contend  that  the  primordial  ele- 
mentals  possess  characteristics  and  qualities  which  differen- 
tiate one  elemental  from  another,  and  that  the  great  diver- 
sity manifest  in  the  physical  universe  cannot  be  accounted 
for  by  mere  number  and  mechanics. 

We  realize  fully  the  lack  of  continuity  and  convincing 
clearness  which  has  been  inevitable  because  of  the  brevity 
of  this  exposition.  This  difficulty  we  hope  to  overcome  in 
the  following  chapters.  We  have  attempted  to  indicate  the 
fundamental  elements  in  a  physical  system  which  depends 
for  its  significance  upon  the  concept  of  God.  We  have  tried 
to  interpret  consistently  the  phenomenal  world  and  its 
activities.  It  is  with  a  full  realization  that  God  knows  better 
that  we  have  presented  this  humble  interpretation  of  His 
create  work. 


CHAPTER  II 
SOME  INCONSISTENT  CONCEPTS  OP  MODERN  SCIENCE 

33.  The  Critique  of  Mathematics. 

Modern  science  overrates  the  value  of  mathematics  in 
the  interpretation  of  physical  phenomena.  In  very  many 
cases  the  results  of  a  mathematical  investigation  are  postu- 
lated as  physical  realities.  There  is  a  great  difference 
between  pure  mathematics  and  applied  mathematics.  Pure 
mathematics  involves  the  forms  of  thought  in  their  relations 
to  space,  time,  and  number.  The  fundamental  premises 
required  in  the  field  of  pure  mathematics  are  grounded  in 
the  content  of  the  rational  mind.  This  is  true  irrespective 
of  the  manner  in  which  this  content  has  developed.  Conse- 
quently the  premises  of  pure  mathematics  are  logically  veri- 
fiable. In  the  field  of  applied  mathematics,  including  phy- 
sical science  and  engineering  science,  the  premises  cannot 
be  verified  through  mere  logic.  They  have  no  value  unless 
they  truly  represent  reality.  The  mathematical  analysis  may 
be  correct,  but  the  result  is  worthless  if  it  does  not  agree 
with  the  facts  of  reality.  This  means  that  the  premises 
were  initially  in  error.  Applied  mathematics,  therefore,  is 
merely  an  experimental  science  by  which  we  test  the  validity 
of  the  initial  premises.  The  final  test  lies  in  the  facts  of 
reality.  The  hypothetical  creations  of  applied  mathematics 
are  mere  fictions  possessing  no  value  unless  they  are  true 
counterparts  of  physical  reality.  Many  of  the  "convenience 
unknowns"  of  physico-mathematics  are  worthless  because 
they  do  not  truly  represent  reality. 

34.  The  Ether. 

The  ether  is  just  such  a  "convenience  unknown."  It 
has  been  adorned  with  "well-defined"  properties.  Its  phy- 
sical content  has  been  determined  by  the  "rigorous  method 
of  mathematics."  Imagine,  for  a  moment,  the  reliability 

45 


46  SCIENTIFIC  THEISM 

of  such  a  farcical  procedure !  Despite  the  fact  that  no  phy- 
sical counterpart  for  the  ether  has  even  been  discovered, 
nevertheless  the  ether  advocate  knows  both  what  it  does 
and  what  it  is.  Of  course,  it  may  be  many  things,  some  of 
which  involve  extraordinary  inconsistencies — in  fact,  self- 
contradictions  of  such  gross  proportions  that  if  the  ether 
were  any  of  these  alleged  "somethings"  it  could  not  con- 
sistently possess  certain  other  properties  imputed  of  vital 
importance  to  its  physical  structure.  The  ether  is  an  infer- 
ential unknown.  Unlike  matter,  the  ether  cannot  be 
observed  by  the  senses.  Consequently  the  physicist  who 
ascribes  definite  properties,  qualities,  and  mathematical 
content  to  the  ether  enters  the  very  zone  of  speculation 
which  he  holds  in  such  ill-repute. 

35.  Force. 

When  we  consider  the  prevailing  scientific  notion  of 
force  we  are  confronted  with  a  concept  which  is  placed  by 
science  in  the  category  of  "what  they  do"  factors.  Through 
this  expedient  the  physicist  hopes  to  avoid  the  responsibility 
of  defining  his  "convenience  unknown."  Questions  relative 
to  "what  it  is"  are  lightly  set  aside  as  irrelevant  even  if 
somewhat  irritating.  Scientists  seem  to  be  in  perfect  accord 
with  one  another  in  defining  force  as  that  which  tends  to 
produce  change  in  the  state  of  rest  or  motion  of  matter. 
Physicists  primarily  regard  force  as  the  "mover"  of  matter, 
the  active  dynamic  factor  in  the  physical  universe,  an  entity 
distinct  from,  but  capable  of  acting  upon,  that  other  inde- 
pendent entity  called  matter.  We  are  here  confronted  with 
a  dualism  of  matter  and  force.  Has  it  been  possible  for 
science  to  adhere  strictly  to  its  self-imposed  attitude  of 
refusing  to  consider  the  problem  of  what  force  is? 

36.  Tubes  of  Force. 

Maxwell  and  J.  J.  Thomson,  employing  the  primary  con- 
cept of  Faraday's  lines  of  force,  developed  systems  which 
make  it  possible  to  consider  mathematically  the  quantitative 
relations  obtaining  in  magnetic  and  electric  phenomena. 
J.  J.  Thomson,  in  attempting  to  visualize  the  activity  factor 
called  force  by  science,  adopts  the  electric  line  of  force  as 


SCIENTIFIC  THEISM  47 

the  unit  from  which  the  so-called  Faraday  tubes  of  force 
are  constructed.  He  considers  a  charged  body  (whatever 
that  is)  to  have  its  external  surface  divided  into  small  areas, 
each  exhibiting  the  same  amount  of  charge.  Emanating 
from  the  boundary  lines  of  these  small  areas  are  lines  of 
force  which  enclose  regions  of  tubular  configuration  consti- 
tuting the  Faraday  tubes.  The  system  is  completed  and 
becomes  active  when  a  second  body  is  introduced  upon 
whose  surface  the  other,  previously  unemployed,  ends  of 
the  lines  of  force  can  rest.  These  opposite  ends,  immedi- 
ately upon  the  entrance  of  the  second  body  into  the  system, 
seek  out  areas  upon  its  surface;  arranging  themselves 
methodically  along  the  boundary  lines.  This  performance 
is  concomitant  with  the  appearance  of  an  electric  charge 
upon  the  small  areas  of  the  second  body.  This  secondary 
electric  charge  upon  the  small  areas  bounded  by  the  tubes 
is  of  equal  magnitude  but  opposite  in  nature  to  the  charge 
upon  the  surface  of  the  first  body.  We  are  curious  to  learn 
if  the  secondary  charge  either  lurked  in  the  vicinity  of  the 
second  body  or  within  its  confines  before  the  tube  pounced 
upon  its  victim.  Perhaps  this  secondary  charge  was  merely 
a  possible  charge  which  became  real  the  moment  the  tube 
touched  the  surface.  Possibly  we  ought  to  consider  that  it 
is  the  tube  that  constitutes  the  charge  and  that  the  two 
ends  thereof  agree  to  differ.  We  may  be  unfair  in  our 
questions;  for,  is  not  the  word  "concomitant"  sufficiently 
awe-inspiring  to  prohibit  levity  in  any  form,  and  cannot 
so  potent  a  word  annihilate  all  tendencies  to  inquire  into 
physical  antecedents  and  relationships?  In  fact,  it  is  main- 
tained that  all  that  is  meant  by  a  charge  on  a  body  is  that 
a  Faraday  tube  ends  upon  its  surface.  Moreover,  the  motion 
of  a  Faraday  tube  is  what  constitutes  the  flow  or  passage 
of  an  electric  current.  This  hypothesis  regards  the  phe- 
nomena of  electrostatics  as  cases  of  tubes  at  rest.  The 
notion  that  opposite  charges  exist  at  the  opposite  ends  of 
the  tubes  involves  the  hypothesis  in  difficulties  which  have 
made  it  necessary  to  modify  the  original  conception,  result- 
ing in  the  supposition  that  each  charge  is  attached  to  a  dis- 
tinct and  separate  tube  which  is  its  own  individual  prop- 
erty. A  charged  body  differs,  then,  from  an  uncharged 
body  merely  in  the  fact  that  the  charged  body  carries  a 


48  SCIENTIFIC  THEISM 

supply  of  Faraday  tubes  protuding  from  its  surface  much 
like  the  quills  of  a  porcupine.  A  Faraday  tube  cannot  be  a 
general  prototype  of  force,  because  if  such  is  the  case,  then 
every  physical  phenomenon  involving  a  manifestation  of 
force  would  also  exhibit  that  physical  or  metaphysical  some- 
thing called  a  charge.  Consequently  force  in  the  form  of  a 
tube  must  be  a  distinct  force  species  which  exhibits  an 
electrical  charge.  A  charge-tube,  then,  is  as  distinct  a  type 
among  force  forms  as  the  porcupine  is  among  animals.  A 
cross  section  of  a  Faraday  tube,  no  matter  where  taken, 
exhibits  merely  lines  of  force.  The  cross  sections  may  differ 
in  their  form  and  size,  but  not  in  the  fact  that  an  area  is 
bounded  by  lines  of  force.  Nevertheless,  we  are  requested 
to  concentrate  our  attention  upon  the  ends  of  the  tubes, 
for  it  is  there  that  the  charge  either  resides  or  appears. 
However,  a  material  aggregate  is  necessary  for  the  appear- 
ance of  the  hidden  factor  called  the  charge.  We  are  de- 
cidedly out  of  order  if  we  impertinently  inquire  whether  the 
charge  is  located  somewhere  in  the  tube,  or  somewhere  in 
the  body,  or  possibly  in  neither  tube  nor  body.  Possibly  the 
hole  in  the  end  of  the  tube  constitutes  the  charge.  Perhaps 
the  particular  shape  of  the  tube  end  is  an  electrical  charge. 
It  may  be  that  the  tube  is  like  a  magic  wand,  and  that  the 
moment  it  touches  a  matter  aggregate  a  charge  ap- 
pears. If  this  is  true  we  ought  not  to  insist  upon  knowing 
the  wherefrom  or  nature  of  the  charge,  for  that  is  not  cus- 
tomary in  fairyland. 

The  tube  itself  must  be  in  its  real  essence  entirely  dis- 
tinct from  matter.  The  lines  of  force  must  not  be  thought 
of  as  a  definite  configuration  of  material  particles,  for  such 
a  conception  would  make  the  term  superfluous.  The  lines 
should  be  considered  as  being  spatial  stress  directions  inde- 
pendent of  the  presence  or  absence  of  matter  in  the  path 
of  stress.  Do  the  tube  advocates  remain  content  with  this 
notion?  We  are  told  that  tubes  of  force,  in  order  to  play 
their  role  properly,  must  be  considered  as  being  subjected 
to  tension  in  a  longitudinal  direction,  thus  producing  a 
decrease  in  the  length  of  the  tube.  When  the  ends  of  the 
tube  lie  upon  a  body  which  is  insulated,  this  contraction  is 
considered  as  being  impossible  of  accomplishment  because 
the  ends  are  so  firmly  fixed  to  the  insulated  body  that  with- 


SCIENTIFIC  THEISM  49 

drawal  is  impossible.  A  splendid  mechanical  model  of 
this  latter  case,  if  this  is  desired — and  it  seems  to  be  the 
sole  purpose  of  the  tube  notion — can  be  constructed  by 
using  wire  to  represent  the  lines  of  force  and  hollow  bodies 
for  the  charged  bodies.  If,  then,  the  wires  are  riveted  on 
the  inside  of  these  shell-like  bodies,  we  have  the  case  of 
tubes  of  force  attached  to  insulated  bodies.  The  fact  is  that 
some  such  notion  must  actually  accompany  this  concept,  for 
how  can  we  otherwise  conceive  the  permanency  of  the  con- 
tact between  tube  end  and  insulated  body?  The  difficulties 
involved  in  this  latter  hypothesis  are  trivial  in  comparison 
with  the  notion  of  a  state  of  tension  existing  along  the 
length  of  the  tube.  We  can  readily  conceive  of  a  state  of 
tension  existing  along  some  particular  line  in  a  material 
body,  in  which  case  science  at  once  introduces  the  term 
"force,"  or  some  similar  term,  to  account  for  the  existence 
of  this  particular  type  of  disturbance.  Are  we,  then,  not 
well  within  our  rights  if  we  demand  that  the  tube  advocates 
exhibit  to  us  a  secondary  force  as  the  real  activity  agent 
in  this  phenomenon  of  force  tube  tension?  Thinking  in 
these  scientific  terms,  it  would  not  be  entirely  inconceivable 
to  imagine  the  case  of  a  tube  of  force  contracting  under 
the  influence  of  an  external  force  influence,  provided  that 
we  did  not  inquire  how  this  phenomenon  would  be  accom- 
plished. 

To  remain  a  scientist  and  think  that  the  tube  of  force 
could  contract  itself  would  be  far  more  inconceivable.  It 
would  be  far  more  consistent  to  refrain  from  materialistic 
particularization  and  be  content  with  the  notion  of  force  as 
synonymous  with  a  deiform  mover  which,  when  acting  upon 
material  groups,  can  cause  them  to  approach  each  other  or 
depart,  depending  upon  the  exigencies  of  the  case.  How- 
ever, this  would  not  be  a  scientific  attitude,  for  in  science 
something  always  acts  upon  something  else  in  accordance 
with  the  principle  of  conservation.  It  would  be  nothing 
less  than  scientific  heresy  to  assume  that  a  given  something 
can  act  upon  itself — indeed,  must  act  upon  itself — before 
it  can  produce  effects  upon  things  other  than  itself.  Never- 
theless, the  Thomsonian  tube  hypothesis  does  just  this.  In 
his  desire  to  visualize  this  particular  group  of  phenomena, 


50  SCIENTIFIC  THEISM 

Thomson  requests  us  to  pin  our  faith  in  the  first  place 
upon  the  tube's  ability  and  willingness  to  contract ;  then  we 
are  properly  prepared  to  accept  the  second  part  of  the  per- 
formance, which  pertains  to  a  spatial  change  of  position 
of  the  involved  material  groups.  It  may  be  that  Thomson 
belongs  to  that  school  of  physics  which  denies  dealing  with 
causes.  If  this  is  the  case,  the  contraction  of  the  tube  would 
be  designated  as  being  the  physical  antecedent  of  the  sub- 
sequent observable  modifications  in  the  matter  groups. 

At  one  time  it  was  considered  sound  reasoning  to  sup- 
pose that  the  earth  was  sustained  by  a  large  tortoise.  This 
one  in  turn  was  supported  by  another  and  larger  one,  and 
so  on  ad  infinitum — which  means  until  you  become  weary 
of  asking  the  same  question  over  and  over  again  and  receiv- 
ing the  same  answer.  Finally,  when  your  patience  is 
exhausted,  the  elephant  is  brought  upon  the  scene  and  the 
last  tortoise  is  then  gently  placed  upon  the  back  of  this 
most  adequate  beast,  whose  ability  to  carry  the  burden  of 
the  proof  must  remain  unquestioned. 

If,  however,  the  Thomsonian  tube  is  the  first  and  only 
tortoise,  then  we  can  clearly  understand  why  the  occult 
power  of  self-contraction  must  be  ascribed  to  it.  This 
power  alone  is  not  a  sufficient  equipment  for  a  well-behaved 
tube.  It  must  be  able  to  distinguish  and  discern  between 
matter  groups,  it  must  be  able  to  play  a  definite,  consistent 
role  in  the  scheme  of  things ;  in  fact,  it  must  be  a  knowing, 
conscious  organization,  otherwise  it  may  readily  be  con- 
ceived that,  at  some  ill-chosen  moment,  the  tube  would  fail 
to  perform  in  a  decorous  manner,  or  cease  its  functioning 
entirely. 

Thomson,  therefore,  in  finding  it  necessary  to  ascribe 
the  function  of  self-contraction  to  the  tube,  has  entered  the 
sphere  of  "what  force  is."  If  that  is  metaphysics,  then 
Thomson  is  a  metaphysician.  It  may  be  retorted  that 
Thomson  is  well  within  the  bounds  of  the  "what  it  does," 
for  in  his  very  assumption  he  merely  maintains  that  the 
tube  "does  contract."  A  fine  quibble,  indeed! — for  what 
can  be  meant  scientifically  by  "what  it  does"  except  the  dis- 
turbing influence  of  the  "it"  upon  other  things  or  "its"  in 
a  genuine  objective  world.  Consequently,  if  the  "it"  does 
something  to  itself,  then  the  scientist  has  ceased  to  deal  with 


SCIENTIFIC  THEISM  51 

the  cold,  unconscious  factors  of  a  material  universe,  and  he 
has  inadvertently  hurled  himself  into  the  domain  of  the 
volitional  and,  at  least,  selective  consciousness. 

37.  The  Erroneous  Dualism  of  Science. 

The  phenomenal  world  for  Thomson  is,  then,  dualistic 
in  its  final  analysis.  Phenomena  are  the  products  of  the 
action  of  force  upon  matter.  Mathematically  considered, 
force  is  a  compound  unit  involving  the  product  of  mass  and 
acceleration.  This  mathematical  definition  can  mean  noth- 
ing if  it  does  not  mean  that  the  magnitude  of  a  "force"  is 
measured  by  the  accelerative  effect  which  it  exerts  upon  a 
given  quantity  of  matter.  Force,  then,  is  an  inferential 
causal  factor  in  the  phenomenal  series.  The  overcoming  of 
force  through  distance  is  known  in  physical  science  as 
"work,"  while  the  ability  to  perform  work  is  classified 
under  the  category  of  "energy." 

We  challenge  the  correctness  of  the  dualistic  position 
which  regards  force  and  matter  as  two  distinct  entities. 
We  maintain  that  the  only  consistent  position  is  the  one 
which  admits  the  identity  of  the  two  in  a  genuine  monon, 
or  force  center. 

38.  Matter  and  Force. 

This  problem  is  not  a  product  of  modern  science.  It 
dates  back  to  the  earliest  thought  of  which  we  have  any 
records.  The  problem  of  matter  and  force  has  interested 
the  human  intellect  from  time  immemorial.  The  early 
thinkers  asked  themselves  the  question,  What  is  the  nature 
of  matter  and  what  are  the  ultimate  constituents  of  mate- 
rial things  and  objects?  Observations  of  matter  in  motion, 
in  contradistinction  to  matter  at  rest,  led  to  the  concepts 
of  cause  and  effect.  A  causal  principle  was  required  to 
account  for  the  change  of  state  from  rest  to  motion.  Hence 
the  invention  of  a  second  principle  or  entity  called  "force" 
by  modern  science.  The  more  primitive  notions  were  veiled 
in  a  mythological  atmosphere.  The  manifestations  of  force 
or  energy  were  regarded  as  the  work  of  gods  or  demons. 
Systems  of  philosophy  arose  later  dealing  with  the  prob- 
lems of  matter  and  force.  Science  and  philosophy,  physics 


52  SCIENTIFIC  THEISM 

and  metaphysics,  had  not  at  that  time  parted  ways.  Science 
and  philosophy  were  almost  synonymous  in  content  and  pur- 
pose. The  modern  scientific  method,  involving  a  correlation 
and  interpretation  of  experimental  facts,  was  as  yet 
unknown. 

39.    Ancient  Cosmic  Theories. 

About  1200  B.  C.  the  Phoenicians  Sanchoniatho  and 
Ochus  evolved  a  materialistic  conception  of  the  universe. 
The  Stoic  Posidonius  speaks  of  Ochus  as  the  first  originator 
and  enunciator  of  an  atomic  theory  of  matter.  The  Chal- 
deans, Egyptians,  Persians,  and  Chinese  evolved  cosmic 
theories  abounding  and  veiled  in  fable  and  mythology.  In 
India,  many  years  before  Christ,  we  find  the  Brahmins, 
Vedantists,  and  Buddhists  discussing  the  nature  and  signifi- 
cance of  matter.  About  600  B.  C.,  Thales,  the  Greek  philoso- 
pher, reduced  the  world  to  an  original  element,  water,  from 
which  all  things  emanated  and  everything  was  divine.  He 
did  not  attempt  to  define  his  concept,  but  named  it  an&pov. 
About  the  year  500  B.  C.,  there  flourished  at  Elea,  in  Italy, 
a  school  of  thinkers  who  asserted  that  the  world  of  things 
was  one  of  appearance  whose  real  nature  could  be  ascer- 
tained only  through  understanding  and  reason.  Xeno- 
phanes,  the  founder  of  this  school,  held  that  all  things  are 
eternal  and  immutable.  To  account  for  the  multifarious 
changes  in  things,  he  assumes  as  primitive  elements  water 
and  earth.  Parmenides,  also  of  the  Eleatic  School,  distin- 
guished between  apparent  knowledge  and  true  knowledge. 
Apparent  knowledge  came  through  the  senses,  while  real 
knowledge  resulted  through  reason.  To  account  for  the 
changes  in  the  physical  universe  he  introduced  two  prin- 
ciples, that  of  heat  or  light,  a  positive  element,  and  that  of 
cold  or  darkness,  a  negative  element,  or,  as  he  preferred  to 
style  it,  a  limitation.  In  the  philosophies  of  the  East  Indians 
we  also  find  the  concepts  of  affirmation  and  negation  play- 
ing an  important  role.  It  remained  for  Hegel  to  round  these 
thoughts  into  a  comprehensive  system. 

Heracleitus,  a  profound  thinker  of  the  Ionian  School, 
also  made  it  his  object  to  discover  an  elemental  principle 
which  he  assumed  to  be  fire,  because  this  was,  for  him,  the 
most  subtle  and  active  of  all  the  elements.  Fire,  he  main- 


SCIENTIFIC  THEISM  53 

tained,  was  at  the  foundation  of  all  things,  and,  conse- 
quently, it  was  the  universal  agent  in  change.  According 
to  Heracleitus,  the  universe  was  neither  the  work  of  gods 
nor  of  men,  but  consisted  in  this  elemental  fire,  which  con- 
tinually kept  alive.  The  changes  noted  in  things  he 
attributed  to  fire,  which  caused  formation  as  well  as  disso- 
lution. The  important  fact  in  the  universe  was  this  very 
transformation,  change,  or  flux  of  things.  Becoming,  not 
being ;  change,  not  static  existence,  was  the  essence  of  that 
which  constitutes  the  reality  of  the  universe. 

Leucippus,  a  contemporary  of  Parmenides,  about  500 
B.  C.,  announced  an  atomic  theory  of  matter.  The  world,  as 
seen  by  Leucippus,  consisted  of  a  countless  number  of 
imperceptibly  small  particles  that  differed  only  in  form, 
position,  and  size.  Leucippus  called  these  particles  dropoi, 
or  atoms.  To  them  he  ascribed  the  power  of  self-motion. 
Whirls  and  vortices  were  formed  by  the  coming  together  of 
these  darting,  moving  particles.  Thus  entire  worlds  were 
formed.  The  nebular  hypothesis  of  Kant,  Laplace,  and 
Swedenborg  was,  consequently,  antedated  by  Leucippus  by 
some  2,200  years. 

Democritus,  the  brilliant  disciple  of  Leucippus,  main- 
tained that  inertia,  or  degree  of  mechanical  movability,  den- 
sity and  hardness  were  properties  of  things.  From  the  two 
fundamental  concepts  of  matter  and  motion,  Democritus 
built  his  world  system. 

After  the  time  of  Democritus,  very  little,  if  any,  advance 
was  made  in  the  theory  of  atomism  until  in  the  sixteenth 
century  A.  D.,  when  the  Italian  Giordano  Bruno  connected 
his  conception  of  the  monad  with  that  of  the  atom  of 
Leucippus. 

It  remained  for  Leibnitz,  the  inventor  of  the  infinitesimal 
calculus  and  the  originator  of  the  conception  of  "vis  viva," 
to  perfect  the  notion  of  a  force  substance  in  his  Monadology. 
The  monad  of  Leibnitz  is  essentially  a  center  of  force.  He 
sought  the  ground  of  the  motion  of  bodies  not  in  their 
extension  and  mass,  but  in  their  ability  to  do  work. 

The  brilliant  Jesuit  mathematician,  physicist,  and 
astronomer,  Father  Boscovich,  with  keen  prophetic  vision, 
developed  the  concept  of  the  force  center  to  its  fullest  excel- 
lence. In  more  recent  times  we  find  Ampere*  Faraday,  and 


54  SCIENTIFIC  THEISM 

Fechner  advocating  this  same  theory  in  certain  phases  of 
their  thinking. 

40.  Dalton's  Atom. 

In  the  year  1803,  Dalton,  employing  the  modern  scientific 
method,  introduced  the  "Law  of  Multiple  Proportions," 
thus  giving  a  fixity  and  definite  individuality  to  the  atom. 
Avogardo,  employing  the  scientific  method,  introduced  into 
science  a  new  term,  the  "molecule,"  in  distinction  from  the 
term  "atom." 

*4 

41.  Kaufmann's  Researches. 

The  fixedness  given  to  the  notion  of  mass  by  the  contri- 
butions of  Dalton  and  Avogadro  was  forever  shattered  by 
the  brilliant  researches  on  Beta  rays  by  Kaufmann  (1902- 
1906) .  Kaufmann  showed  that  as  the  velocity  of  the  Beta 
particles  approached  that  of  light,  the  mass  of  the  particles 
approached  an  infinite  magnitude.  The  common  inference 
from  this  discovery  is  that  an  infinite  force  is  necessary  to 
give  to  a  particle  the  velocity  of  light ;  and,  furthermore,  the 
erroneous  conclusion  is  that  light  cannot  be  a  manifestation 
of  material  particles. 

42.  The  Two  Alien  Entities  of  Science. 

In  its  atomistic  garb,  matter  assumed  such  dignity  and 
importance  that  the  notion  became  the  father  of  the  modern 
materialistic  school  of  philosophy.  Matter  in  motion,  how- 
ever, as  the  paramount  datum  of  experience,  proved  itself 
a  difficult  notion  for  science  to  solve.  The  idea  of  activity 
of  matter  contained  a  further  notion  of  a  factor  unlike  mat- 
ter yet  operating  in  conjunction  with  matter,  producing  the 
phenomena  of  motion  of  matter  in  space.  The  primary 
experience  datum  has  the  semblance  of  a  compound  com- 
posed of  a  distinct  and  independent  active  factor  and 
another  separate  entity  whose  nature  is  wholly  passive. 
The  term  "energy"  has  been  introduced  by  science  in  order 
to  place  an  exact  label  upon  the  active  factor.  We  find  the 
term  "force"  used  frequently  in  a  synonymous  sense  to  des- 
ignate the  activity  factor  in  the  universe.  The  exact  scien- 
tific definition  of  energy  involves  two  factors,  mass  and  the 


SCIENTIFIC  THEISM  55 

square  of  the  velocity  together  with  the  constant  y%; 
while  force  is  defined  as  the  product  of  mass  and  accelera- 
tion. The  independent  activity  factor,  whether  it  be  called 
energy  or  force,  is  defined  by  physics  in  terms  of  the  other 
independent  and  passive  factor  mass.  Science  by  this  very 
act  admits  the  impossibility  of  isolating  the  two  factors  as 
independent  existences,  nevertheless,  by  universal  consent 
they  are  so  regarded.  The  Faraday  tube  of  force,  previously 
considered,  is  a  definite  example  of  how  science  clearly  disso- 
ciates the  two  notions  and  regards  them  as  distinct  entities 
having  equal  claims  upon  reality.  In  order  causally  to 
account  for  physical  phenomena,  science  introduces  an  infer- 
ential X,  a  conceptual  something  to  bridge  the  glaring  gaps 
in  the  physical  series.  Thus  arose  the  dualistic  theory  of 
matter  and  force  as  the  two  separate  entities  from  whose 
mutual  action  phenomena  are  produced.  The  task  of 
science  has  been  to  arrange  an  act  between  these  two  enti- 
ties, perhaps  alien  and  inimical  in  their  real  nature,  upon 
the  stage  of  phenomenal  experience,  with  space,  time,  and 
causality  as  the  scenery.  The  task  has  proved  of  herculean 
proportions,  and  a  resort  to  a  "psycho-physical"  force  com- 
posed of  kinetic  energy  and  intelligence  cannot  overcome 
the  difficulties  involved,  even  if  such  a  term  be  given  its 
broadest  possible  significance,  if  it  be  regarded  as  an  entity 
or  being  independent  of  matter. 

This  dualistic  theory  continually  involves  science  in  an 
unending  chain  of  difficulties.  Force  must  find  its  way  from 
one  group  of  matter  to  another ;  it  must  make  itself  known 
from  one  material  aggregate  to  another  such  aggregate. 
As  a  consequence  of  these  difficulties  and  problems  there 
arose  the  much  mooted  question  whether  forces  can  make 
themselves  known  at  a  distance  without  the  intervention 
of  a  transmitting  vehicle  or  medium,  or  whether  force 
effects  must  have  a  medium  through  which  they  can  travel 
from  one  group  to  another. 

43.    The  Unifying  Principle. 

In  the  preceding  chapter  we  have  seen  some  of  the  inher- 
ent weaknesses  of  the  materialistic  position.  The  tube-of- 
force  concept  involves  insurmountable  incompatibilities. 
To  make  it  operative  at  all,  selective  intelligence  must  be 


56  SCIENTIFIC  THEISM 

introduced  into  the  notion.  However,  materialism  refuses 
to  countenance  any  conceptual  content  which  involves  some- 
thing other  than  mere  mechanism.  Nevertheless,  "some- 
thing other  than  mere  mechanism"  must  be  introduced  into 
the  groundwork  of  the  universe  in  order  to  explain  physical 
action.  Moreover,  it  is  impossible  to  regard  force  and  mat- 
ter as  independent  entities.  Materialism  has  utterly  failed 
to  show  us  the  modus  operandi  by  which  interaction  between 
those  two  alien  entities  may  be  established.  A  unifying 
concept  is  absolutely  necessary  in  order  to  make  physical 
action  possible.  Selective  intelligence,  which  even  the  rabid 
materialist  must  include  in  all  his  concepts,  involves  the 
admission  that  reason  and  intelligence  constitute  the  founda- 
tions of  the  cosmos.  In  the  world  of  purely  physical  phe- 
nomena determinism  governs  activity.  The  physical  uni- 
verse is,  consequently,  a  world  of  secondary  causes.  There- 
fore, we  do  not  countenance  the  idea  held  by  some  thinkers 
that  selective  intelligence  involves  conscious  will.  The  phy- 
sical elementals  of  the  universe  give  us  no  indication  of  the 
slightest  trace  of  conscious  life.  Therefore  we  are  forced 
to  the  conclusion  that  the  imprint  of  deterministic  character 
exhibited  by  the  physical  elementals  is  an  endowment  as- 
signed to  them  by  the  Creative  Divine  Intelligence.  The 
deterministic  characteristics  of  the  primordial  elementals 
are  merely  a  part  of  those  unified  rational  activity  relations 
which  we  record  as  the  physical  story  of  a  rational  cosmos. 
Consequently  this  record  is  written  in  terms  of  natural  laws. 
In  the  introductory  chapter  we  have  shown  that  the  admis- 
sion that  reason  and  intelligence  are  necessary  for  the  expla- 
nation of  physical  phenomena  involves  the  further  admis- 
sion of  the  existence  of  a  Creative  Divine  Intelligence.  Fur- 
thermore, the  concept  of  God  furnishes  us  with  the  only 
unifying  principle  capable  of  accounting  for  the  law- 
ordained  interaction  between  primordial  elementals  which 
would  be  incapable  of  such  intelligible  interaction  if  they 
are  regarded  as  the  independent  entities  erroneously  isolated 
by  materialistic  science. 


CHAPTER  III 
ACTION  AT  A  DISTANCE  AND  THE  ETHER  HYPOTHESES 

44.     Action  at  a  Distance. 

Some  two  hundred  and  fifty  years  ago,  the  scientific 
world  found  it  difficult  to  conceive  the  idea  that  matter  can 
act  where  it  is  not.  At  that  time  the  motions  of  the  planets 
were  explained  by  a  mechanism  of  cycles  and  epicycles. 
This  system  was  slightly  improved  by  Descartes,  the  French 
philosopher  and  mathematician,  by  introducing  the  concep- 
tion of  "vortices."  At  the  time  of  its  introduction  to  the 
scientific  world,  the  Newtonian  doctrine  of  gravitational 
attraction  met  with  stubborn  resistance.  In  a  letter  written 
by  Voltaire  in  the  year  1727  reference  is  made  to  this  resist- 
ance. Voltaire,  having  just  visited  England,  wrote:  "A 
Frenchman  who  arrived  in  London  finds  a  great  alteration 
in  philosophy,  as  in  other  things.  He  left  the  world  full ;  he 
finds  it  empty.  At  Paris  you  see  the  universe  composed  of 
vortices  of  subtile  matter ;  at  London  we  see  nothing  of  the 
kind.  With  you  it  is  the  pressure  of  the  moon  which  causes 
the  tides  of  the  sea ;  in  England  it  is  the  sea  which  gravitates 
toward  the  moon.  You  will  observe  also  that  the  sun,  which 
in  France  has  nothing  to  do  with  the  business,  here  comes 
in  for  a  quarter  of  it.  Among  you  Cartesians  all  is  done 
by  impulsions ;  with  the  Newtonians  it  is  done  by  an  attrac- 
tion of  which  we  know  the  cause  no  better." 

The  much  mooted  question  of  action  at  a  distance  dis- 
turbed the  scientific  world  over  two  hundred  years  ago 
and  divided  it  Into  two  camps. 

Stated  concisely,  the  question  is,  Can  matter  act  where 
it  is  not?  Must  discrete  portions  of  matter  be  connected 
by  an  intermediate  something,  an  X,  a  medium,  plenum, 
or  ether,  by  means  of  which  one  material  system  can  be 
placed,  as  it  were,  en  rapport  with  another  distant  material 
system?  Daniel  Bernoulli  answered  the  former  question 
in  the  affirmative  and  denied  the  necessity  of  a  gravific 

57 


58  SCIENTIFIC  THEISM 

medium  in  a  letter  written  in  1744  to  the  mathematical 
physicist  Euler.  Father  Boscovich,  in  a  work  entitled  "The- 
oria  Philosophia  Naturalis,"  published  at  Vienna  in  1758, 
maintained  with  Daniel  Bernoulli  that  action  at  a  distance 
was  possible  through  an  absolute  vacuum.  For  him  matter 
consisted  merely  of  force  centers  endowed  with  inertia,  and 
all  physical  and  chemical  activities  were  explainable  as 
mutual  attractions  and  repulsions,  varying  in  intensity  with 
the  magnitude  of  the  intervening  distance. 

45.  The  Medium  of  Faraday. 

Later  the  brilliant  investigator,  Faraday,  combated 
the  doctrine  of  Bernoulli  and  Boscovich  and  infused  new 
life  into  the  medium  hypothesis  by  his  researches  into  elec- 
trical and  magnetic  phenomena.  In  fairness  to  Faraday 
we  must  quote  the  following,  in  which  he  refers  to  the  notion 
of  a  corporeally  extended  atom :  "What  do  we  know  of  the 
atom  apart  from  its  force?  You  imagine  a  nucleus  which 
may  be  called  a,  and  surround  it  by  forces  which  may  be 
called  ra;  to  my  mind,  the  a,  or  nucleus,  vanishes  and  the 
substance  consists  of  the  powers  m.  And,  indeed,  what 
notion  can  we  form  of  the  nucleus  independent  of  its  pow- 
ers? What  thought  remains  on  which  to  hang  the  imagi- 
nation of  an  a  independent  of  the  acknowledged  forces?" 
This  is  a  most  remarkable  and  clear  statement  of  what 
everyone  must  admit  is  the  true  condition  of  our  knowledge 
of  corporeality.  However,  Faraday's  difficulty  consisted  in 
arranging  mutual  action  between  these  force  centers.  He 
therefore  advocated  the  notion  of  a  medium  as  the  necessary 
link  which  could  make  possible  mutual  action  between  force 
centers. 

46.  The  Ether  of  Clerk-Maxwell  and  Hertz. 

The  cause  of  the  ether  hypothesis  was  furthered  by  the 
mathematical  investigations  of  Clerk-Maxwell  and  by  the 
researches  of  Heinrich  Hertz  upon  the  velocity  of  propaga- 
tion of  electro-magnetic  effects.  The  conception  of  electro- 
magnetic propagation  in  the  ether  is  due  principally  to  the 
nineteenth-century  school  of  physicists. 

The  advent  of  the  corpuscular  or  electronic  theory  of 


SCIENTIFIC  THEISM  59 

matter  has  cast  doubt  upon  the  efficacy  of  a  plenum  or 
ether  hypothesis  to  explain  the  many  new  phenomena  dis- 
covered in  the  domain  of  electrophysics  and  electro- 
chemistry. 

47.    The  Field  of  Force  and  its  Implications. 

The  followers  of  Faraday  and  Clerk-Maxwell  still  con- 
tinue to  deny  the  possibility  of  action  at  a  distance  and 
assert  that  electrostatic  and  magnetic  attractions  and  repul- 
sion are  due  to  the  stress  or  pressure  action  of  a  field  of 
force  which  surrounds  charged  or  magnetized  bodies. 

It  is  pertinent  to  ask  the  followers  of  Faraday  what 
they  mean  by  the  term  "field  of  force."  Is  it  a  reality  in 
the  external  world,  or  is  it  merely  a  thought  phantom  con- 
jured into  merely  conceptual  existence  as  a  mathematical 
necessity?  If  we  read  about  "field  of  force"  in  works  on 
electricity  and  repeat  the  term  a  sufficient  number  of  times, 
it  becomes,  after  a  while,  a  mental  friend  which  assumes, 
perhaps,  unwarranted  proportions  of  reality.  Add  to  this 
pictorial  illustrations  of  "tubes  of  force"  bedecked  and 
adorned  with  mathematical  symbols  of  exactness  and  final- 
ity, and  we  are  brought  face  to  face  with  a  powerful 
Goliath  able  to  crush  out  and  extinguish  those  impulses  of 
common  sense  which  demand  a  counterpart  in  the  physical 
world  for  the  magic  phantoms  of  a  fertile  mathematical 
imagination. . 

Two  possible  answers  present  themseles  to  my  mind 
like  the  horns  of  a  dilemma.  On  the  one  hand,  the  followers 
of  Faraday  can  maintain  that  by  "field  of  force"  they  mean 
an  active  energized  ether — whatever  that  is — or,  on  the 
other,  they  may  hold  that  the  term  is  merely  a  mathematical 
invention,  a  conceptual  creation  in  the  nature  of  a  last 
resort  when  face  to  face  with  problems  of  ultimate  reality. 
There  are  many  who  do  not  hesitate  to  label  such  conceptual 
creations  as  "metaphysical"  plus  a  tinge  of  pity  and  scorn 
for  the  originator :  a  most  curious  attitude,  in  view  of  the 
fact  that  science  itself  is  replete  with  metaphysical  con- 
ceptions which  pertain  to  hypothetical  causal  factors  not 
known  to  sense  perception.  However,  since  "field  of  force" 
is  a  well-established  scientific  term  possessed  of  a  perfectly 
respectable  ancestry,  we  are  given  to  understand  that  we 


60  SCIENTIFIC  THEISM 

must  be  very  careful  lest  we  commit  the  unforgivable  sin 
of  assigning  this  term  to  the  category  of  the  metaphysical. 

Let  us  assume,  then,  that  "field  of  force"  is  not  a  "meta- 
physical" will-o'-the-wisp  changing  with  the  physico-mathe- 
matical  fashions,  but  that  it  is  a  genuine  reality  in  the 
external  world  capable  of  performing  the  gyrations  and 
contortions  required  of  it  by  physical  phenomena.  An 
inquiry  into  the  nature  of  this  reality  is  then  pertinent. 
Is  "field  of  force"  matter?  Is  it  non-matter  (shall  we  say 
spirit,  soul,  ultimate  essence,  absolute,  or  what  not?) ;  or 
is  it  a  subtile  something  neither  matter,  as  known  to  our 
senses,  nor  vacuum,  meaning  complete  absence  of  matter? 
Shall  we  take  the  term  at  its  face  value,  and  suppose  that 
the  three-dimensional  expanse  of  space  is  the  sporting 
ground  of  forces  which  romp  and  prance  about,  at- 
taching themselves  ever  and  anon  to  alien,  uninterested 
particles  of  matter  whose  nature  is  antipodal  to  that  of 
force  ? 

If  the  field  of  force  is  composed  of  matter,  then  the 
nature  of  the  stress  exerted  by  it,  which  is  assumed  to  be 
the  cause  of  the  attraction  or  repulsion,  must  be  explained. 
In  other  words,  the  mechanism  by  which  surrounding  mat- 
ter causes  stress  or  pressure  to  be  exerted  upon  the  sur- 
rounded matter  must  be  shown.  Even  if  this  be  possible, 
we  are  at  a  loss  to  know  what  advantage  has  been  gained 
by  substituting  the  term  "stress"  for  that  of  attraction. 
It  seems  that  one  inexplicable  term  is  of  as  little  value  as 
another,  or  even  as  any  third  which  can  be  invented  as  a 
substitute  for  both. 

Suppose  that  we  assume  that  the  field  of  force  is  a  sub- 
tile something,  neither  matter  nor  non-matter,  but  a  plenum, 
medium,  or  ether.  This  assumption  leads  us  to  the  consid- 
eration of  the  continuity  or  discontinuity  of  matter.  If  we 
maintain  that  matter  exists  continuously  throughout  space, 
and  we  still  find  need  for  an  ether  to  perform  activities  un- 
assignable to  matter,  then  we  are  forced  to  hold  that  ether 
and  matter  coexist  in  the  same  space.  This  thought,  aside 
from  being  repugnant  to  sound  reasoning,  involves  so  many 
difficulties  even  for  the  ablest  mathematician  that  very  little 
can  be  expected  from  such  an  hypothesis.  We  must  demand 
consistency  from  any  hypothesis.  If  ether  is  a  genuine 


SCIENTIFIC  THEISM  61 

something,  not  force,  energy,  spirit,  or  thought — in  other 
words,  a  real  substance  differing  in  its  nature  from  matter, 
yet  actually  existing  in  space,  which  involves  occupancy  of 
space — then  ether  and  matter  cannot  coexist  in  space  even 
if  mathematical  manipulation  can  find  a  way  to  surmount 
the  other  difficulties  involved  in  this  conception.  It  is  folly 
to  expect  a  physical  counterpart  for  every  imaginable  mathe- 
matical expression.  It  is  the  part  of  wisdom  to  condense 
actual  physical  phenomena  to  the  shorthand  of  mathematical 
expressions. 

48.  Matter  Regarded  as  Distinct  from  Ether. 

The  remaining  alternative  is  that  matter  is  discontinuous 
and  that  ether  exists  where  matter  is  not.  We  must  then 
assign  one  set  of  properties  to  matter  and  another  set  to 
ether.  These  properties  must  be  capable  of  taking  mutual 
cognizance  of  each  other.  The  mechanism  by  which  this 
cognizance  becomes  effectively  operative  must  be  set  forth. 
Furthermore,  we  must  assign  to  the  ether  some  definite 
content  if  it  is  to  be  even  a  factor  in  thought.  If  it  is  not 
assumed  to  be  some  form  of  matter — make  it  as  subtile, 
elusive,  rare,  and  minute  as  you  please — then  it  must  be 
placed  in  some  entirely  different  category  from  matter; 
in  other  words,  if  the  ether  is  not  some  form  of  matter,  it 
must  be  akin  in  its  nature  to  force,  energy,  mind,  or  spirit, 
in  which  event  we  eliminate  the  spatial  attribute  entirely. 

49.  Matter  Regarded  as  Ether  in  Motion.    The  Theories  of 
Euler,  Helmholtz,  and  Kelvin. 

In  order  to  obviate  the  difficulties  encountered  in  both 
the  above-mentioned  suppositions,  a  radically  different  solu- 
tion has  been  put  forth  in  recent  years.  This  involves  the 
notion  that  all  is  ether,  that  there  is  no  such  substance  as 
matter  distinct  from  and  independent  of  the  ether,  and  that 
the  ether  is  an  ideal  incompressible  fluid.  Euler  investigated 
mathematically  the  possibilities  of  motion  in  such  an  ideal 
fluid.  He  cared  little,  as  many  other  mathematical  physi- 
cists have  done,  whether  the  physical  counterpart  of  his 
ideal  fluid  could  be  shown  to  exist.  For  him  it  was  a 
thought-phantom,  with  which  to  play  at  the  game  of  mathe- 


62  SCIENTIFIC  THEISM 

matics.  Thought-phantoms  oftentimes  become  genuine 
realities  to  the  best-disciplined  physicists  if  they  happen  to 
meet  mathematical  requirements.  Von  Helmholtz's  consid- 
rations  of  the  ideal  fluid  of  Euler  led  him  to  propound  the 
theorem  that  rotaton,  once  established  in  such  an  ideal  fluid, 
is  unending,  while  particles  which  do  not  rotate  from  the 
beginning  can  never  be  set  in  rotation.  These  doctrines  in 
the  hands  of  Lord  Kelvin  were  developed  into  the  theory  of 
yortex  atoms,  which,  according  to  Kelvin,  are  spinning 
gyrostatic  elements  of  ether  in  the  ether. 

50.  Karl  Pearson's  Ether  Hypothesis. 

Kelvin's  theory,  although  a  most  ingenious  mathematical 
creation,  nevertheless  involves  the  same  insurmountable 
difficulties  as  are  found  in  all  the  ether  hypotheses.  Karl 
Pearson  has  put  forward  another  ether  hypothesis  differing 
from  Kelvin's  in  the  modus  operandi  of  its  atoms,  but  in 
complete  accord  with  him  in  regarding  matter  as  merely 
an  ether  disturbance  in  the  ether.  Karl  Pearson,  however, 
shows  sound  sense  in  disclaiming  external  reality  for  his 
thought  creation,  and  he  distinctly  states  that  the  ether  is 
nothing  more  than  a  conceptual  limit  of  our  perceptual 
experience. 

51.  The  Inconsistent  Content  of  the  Ether  Hypothesis. 
The  ether  is  a  thought  creation  intended  to  bridge  the 

chasm  between  material  bodies  and  particles  and  to  make 
explicable  the  phenomena  of  the  physical  world.  Primarily, 
then,  it  is  a  thought  concept,  an  hypothesis  of  which  we 
must  demand  self -consistency.  All  advocates  of  the  ether 
hypothesis  agree  in  maintaining  that  the  ether  is  a  per- 
fectly homogeneous  fluid  not  made  up  of  discrete  parts  like 
that  other  fluid,  water,  with  which  we  are  so  familiar. 
When  the  discrete  particles  of  water  are  set  in  motion  a 
current  or  stream  of  these  separate  particles  can  be  seen. 
How  can  a  perfectly  homogeneous  fluid  not  composed  of 
separate  parts  ever  make  manifest  to  the  senses  any  changes, 
rotations,  gyrations,  or  displacements  taking  place  within 
it?  The  ether  is  a  weightless  something  filling  all  space. 
It  is  isotropic,  that  is,  it  has  the  same  properties  in  all  direc- 


SCIENTIFIC  THEISM  63 

tions.  It  is  incompressible.  These  properties  are  common 
to  all  ethers,  and  the  brands  are  numerous.  Differences  of 
opinion  exist,  however,  in  regard  to  the  other  properties  of 
the  ether.  Maxwell  gives  the  following  values : 

Density  of  the  ether=  106x10— so  |  (water=unity). 
Modulus  of  rigidity  (in  C.G.S.  units) =955. 
Modulus  of  rigidity  of  glass  in  the  same  units=24x!01-a. 
Density  of  the  ether=  JtJmrinr^piimriTnnr  (air=unity). 
Rigidity =T4Tr,THr™nnr  (glass = unity). 

These  corrected  Maxwellian  values  assume  the  amplitude  of 
an  ether-wave  as  JL  of  its  wave  length.  It  is  equally  cor- 

100  i 

rect  and  admissible  to  assume  the  amplitude  as  100000  of 
its  wave  length.  For  this  supposition  the  density  of  the 

ether  becomes  It0oo,ooo,ooo  of  air  and  its  rigidity  equals  -^ 
of  glass.  The  enormous  inconsistencies  of  the  hypothesis 
make  it  unnecessary  to  split  hairs  in  regard  to  the  decimal 
places  in  the  above  values.  As  a  medium  of  excitation  of 
mathematical  imagination  the  ether  stands  without  a  peer 
in  the  history  of  physical  science. 

If  the  density  ascribed  to  the  ether  is  either  of  the  above 
values,  it  must  be  the  rarest  of  all  gases.  A  gas  of  such 
rarity  cannot  be  imagined  with  discrete  parts  separated  by 
great  distances.  This  conclusion  contradicts  the  assumption 
that  the  ether  is  continuous  throughout  space.  Moreover, 
it  vitiates  the  hypothesis  of  incompressibility.  In  the  face 
of  these  facts,  Maxwell  did  not  hesitate  still  further  to 
torture  the  ether  in  order  to  force  it  to  account  for  gravita- 
tion. Consequently  he  assumed  that  it  was  able  to  withstand 
a  pressure  of  37,000  tons  per  square  inch  in  a  vertical 
direction  and  a  tension  of  the  same  amount  in  a  horizontal 
direction.  When  we  compare  this  with  the  rigidity  of  high 
carbon  steel  having  an  ultimate  strength  of  50  tons  per 
square  inch,  we  wonder  how  it  is  possible  for  bodies  to  move 
about  in  this  all-pervading  ether  with  such  consummate 
ease.  Physico-mathematics  does  not  always  trouble  itself 
with  the  demands  of  common  sense.  It  is  known  that  the 
planets  and  the  atoms  move  through  space  with  a  freedom 
which  forces  us  to  assume  that  it  is  absolutely  empty. 


64 


SCIENTIFIC  THEISM 


52.    A  Critical  Analysis  of  the  Ether  Hypotheses. 

Hertz  has  clearly  set  forth  the  requirements  of  the 
ether  in  order  that  it  shall  be  capable  of  explaining  the  phe- 
nomena of  electromagnetics.  An  impartial  common-sense 
examination  of  the  Hertzian  disquisition  in  regard  to  the 
propagation  of  electric  disturbance  in  the  ether  cannot  result 
in  anything  but  a  verdict  against  the  ether  as  a  rational 
hypothesis  for  the  explanation  of  these  phenomena. 

HYPOTHESIS  I,  CASE  I 

A  logical  analysis  of  the  possible  conceptions  concerning 
the  nature  of  the  ether  brings  before  us  two  distinct 
hypotheses. 

The  first  hypothesis  considers  the  electrical  disturbance 
as  being  due  to  the  combined  action  of  two  distinct  fac- 
tors— a  medium  and  the  effect  of  action  at  a  distance. 

The  basic  postulate  is  that  space  is  nowhere  empty,  but 
is  filled  with  a  mysterious  substance  or  something  called 
ether.  Under  the  first  hypothesis  we  find  two  related  cases. 

First  Factor.  Action  at  a  distance  considered  as  the 
large  factor. 

Second  Factor.  Effect  in  ether  regarded  as  the  small 
factor. 

Assumptions 

It  is  assumed  that  the  acting  force  produces  a  change, 
called  polarization,  in  the  smallest  parts  of  the  medium.  In 
Fig.  1  we  show  diagrammatically  the  conditions  supposed 

ETHER 


No  Polarization. 


Figure  1 


SCIENTIFIC  THEISM  65 

to  obtain  in  Case  I.  In  this  diagram,  A  and  B  represent  two 
oppositely  charged  bodies.  The  intervening  space  is  the 
particular  abiding-place  of  the  ether.  The  small  rectangles 
represent  ether  particles.  The  fact  that  a  different  state 
or  condition  exists  at  the  opposite  extremities  of  these  ether 
particles  is  indicated  by  a  cross-sectioned  surface  and  a  full 
black  surface.  The  space  C  shows  the  existing  conditions 
when  a  portion  of  the  ether  is  removed  in  the  space  between 
the  bodies  A  and  B.  The  positive  and  negative  electricitis 
are  shown  upon  the  two  bodies  A  and  B  by  the  same  conven- 
tional method  used  to  indicate  the  opposite  states  of  polari- 
zation in  the  ether  particles.  The  force  exerted  between  the 
two  bodies  is  indicated  by  arrows.  The  ether  or  electric 
fluid  between  A  and  B  is  regarded  as  an  absolutely  continu- 
ous isotropic  substance.  It  is  supposed  that  if  a  portion  C 
of  the  ether  is  removed  the  forces  within  the  space  C  remain 
unchanged,  but  the  phenomenon  of  polarization  disappears 
with  the  removal  of  the  ether. 

Implications 

Every  ether  hypothesis  insists  upon  the  fact  that  the 
ether  is  a  continuum.  Indeed,  this  is  its  principal  function 
and  purpose  in  physical  science.  In  other  words,  the  ether 
fills  space.  Consequently  human  intelligence  can  readily 
subdivide  the  ether  into  continuum  areas  of  the  most  minute 
dimensions.  A  vacuous  space  can  be  similarly  divided  by 
the  imagination.  However,  we  need  not  expect  more  of  the 
little  imaginary  ether  areas  than  we  expect  of  the  vacuum 
areas.  The  little  ether  areas  will  not  show  animal  propensi- 
ties, they  will  not  perform,  they  will  not  become  individuals, 
they  will  not  polarize  just  because  the  human  imagination 
has  created  them.  Human  imagination  does  not  create  life, 
it  does  not  cause  genuine  entities  possessing  well-defined 
properties  and  functions  to  come  into  being.  If  the  ether 
is  a  continuum,  it  will  always  remain  a  continuum.  If  it 
is  a  discontinuum,  then  it  is  a  form  of  matter,  however 
subtile  and  refined,  and  it  is  then  composed  of  genuine  dis- 
parate physical  parts.  If  it  is  still  maintained  that  distinct 
and  individualized  parts  do  exist  in  this  continuum,  then  the 
ether  advocate  must  not  keep  us  in  total  darkness  in  regard 
to  the  nature  of  that  choice  which  determines  the  physical 


66  SCIENTIFIC  THEISM 

magnitude  of  these  ether  spaces.  Does  the  ether,  by  the  use 
of  intelligent  volition,  determine  the  precise  boundaries  to 
its  own  little  subdivisions?  Are  the  physical  dimensions 
equal  or  unequal?  Is  the  process  one  of  blind  chance,  or 
do  the  bodies  A  and  B  play  a  part  in  the  unique  drama? 
Moreover,  we  are  not  content  with  the  mere  term  "polariza- 
tion" as  an  explanation  of  a  condition  or  state  supposed  to 
come  into  existence  upon  these  subdivisions  if  such  parts 
actually  exist  at  all.  The  very  vagueness  of  the  term  may 
be  the  satisfying  element  to  some,  but  it  should  not  be 
acceptable  to  the  scientist  who  prides  himself  upon  the  won- 
derful mathematical  accuracy  of  all  his  intellectual  inven- 
tions. If  "poralization"  means  anything  at  all  more  than 
a  convenient  highly  unscientific  artifice,  it  must  mean  that 
two  antipodal  conditions  exist  upon  diametrically  opposite 
portions  of  the  little  subdivisions.  Of  the  infinite  number 
of  possible  diameters,  which  one  will  prove  to  be  the  favored 
and  the  chosen?  Does  the  imaginary  subdivision  do  its 
own  selecting  of  such  a  diameter?  Perhaps  the  ether  as  a 
whole  directs  the  maneuver.  Possibly  the  body  A  or  the 
body  B,  or  both,  or  something  entirely  outside  of  the  system, 
exerts  its  potent  intelligent  will  telepathically  in  this  mys- 
terious selection.  All  these  conjectures  may  be  fatuous 
errors.  An  unseen,  seen,  heard,  or  unheard  of  force  may 
be  the  directing  and  guiding  influence  in  this  ethereal  phe- 
nomenon. By  what  mechanism,  may  we  ask,  does  this  force 
produce  changes  in  the  ether  particles?  Our  inquisition  is 
not  complete  unless  we  insist  upon  being  informed  in  regard 
to  the  precise  nature  of  the  two  antipodal  conditions  created 
in  this  homogeneous  isotropic  plenum.  Is  one  condition 
compression  and  the  other  tension  ?  Has  the  ether  substance 
undergone  a  change  in  its  very  nature  so  that  the  antipodals 
are  structural  opposites?  Do  the  diametrically  opposite 
ends  vibrate  at  different  rates  ?  It  may  be  that  a  something 
has  attached  itself  to  one  end,  and  an  entirely  different 
something  has  simultaneously  affixed  itself  to  the  other  end. 
Why  not  assume,  in  order  to  simplify  the  problem,  that  a 
state  of  joy  exists  at  one  end  and  a  state  of  sorrow  holds 
forth  at  the  other?  From  the  standpoint  of  aesthetics  it 
may  prove  more  impressionistic  to  suppose  that  one  end  is 
white  and  the  other  black. 


SCIENTIFIC  THEISM 


67 


It  may  be  said  that  we  are  entirely  too  severe  in  our 
innuendoes.  Drastic  measures,  however,  are  required  to 
subdue  that  spirit  of  intolerance  in  science  which  prohibits, 
either  by  ridicule  or  by  willful  disregard,  the  open,  unbiased 
discussion  of  the  validity  of  the  basic  concepts  which  form 
the  very  foundation-stones  of  science.  The  utter  careless- 
ness with  which  modern  science  creates  new  convenience 
concepts,  without  in  any  way  relating  them  to  a  real  world 
and  without  any  semblance  of  exactitude  and  consistency 
in  the  content  of  such  concepts,  is  certainly  deplorable. 
Intrenched  within  the  fortress  of  experimental  investiga- 
tion, the  scientific  method  can  defy  the  attacks  of  supersti- 
tion and  emotional  traditions.  Nevertheless,  a  consistent 
science,  a  progressive  science,  a  science  of  the  future,  if  it  is 
to  employ  in  its  edifice  concepts  which  bring  it  into  imme- 
diate rapport  with  the  living,  conscious  world  order,  must 
not  ignore  the  logic  of  philosophy  and  metaphysics  in  any 
attempt  to  construct  a  consistent  cosmic  system. 

53.  HYPOTHESIS  I,  CASE  II 

First  Factor.  Action  at  a  distance  considered  as  the 
small  factor. 

Second  Factor.  Effect  in  ether  regarded  as  the  large 
factor.  This  case  is  shown  pictorially  in  Fig.  2. 


ETHER 


No  Polarization 
forces  £"xist 


Figure  2 


68  SCIENTIFIC  THEISM 

Assumptions 

For  this  case  the  action  at  a  distance  effect  is  considered 
as  merely  a  nominal  factor.  The  charges  on  the  bodies  A 
and  B  exist,  but  they  are  small.  It  is  assumed  that  the  elec- 
tricity of  the  medium  is  displaced  toward  the  action  at  a 
distance  effect,  thus  neutralizing  this  latter  effect  to  a  great 
extent.  It  is,  moreover,  supposed  that  the  medium  exerts  a 
pressure  on  account  of  the  attraction  of  its  internal  electri- 
fications, which,  in  turn,  tends  to  draw  the  bodies  A  and  B 
together.  The  forces  are  still  imagined  to  exist  in  the  empty 
space  C,  although  they  are  considered  as  vanishingly  small. 
As  in  Case  I,  no  polarization  is  assumed  in  the  empty  space 
C.  Helmholtz  developed  this  view  for  the  entire  field  of  elec- 
tro-magnetic phenomena.  Poisson  employed  it  for  the  stat- 
ical phenomena  in  magnetism,  while  Mosotti  found  it  useful 
in  the  explanation  of  electrical  phenomena. 

Implications 

What  real,  definite  meaning  shall  we  place  upon  this 
conglomerate  mass  of  words?  It  all  sounds  very  technical, 
abstruse,  and  therefore  very  sane.  Indeed,  we  are  upon 
holy  ground  and  should  have  some  reverence  for  such  glo- 
rious and  profound  words  as  "electricity  of  the  medium," 
"neutralization,"  "internal  electrifications."  Such  wonder- 
ful words  ought  to  possess  sufficient  inherent  power  to  drag 
any  two  bodies  together,  no  matter  what  distance  or  ob- 
stacles may  intervene. 

What  genuine,  clearly  defined  concept  shall  we  affix  to 
the  combination  of  words  "electricity  of  the  medium"? 
While  our  attention  has  been  distracted,  our  friend  the 
scientific  prestidigitator  has  produced,  as  if  from  nowhere, 
another  "convenience  unknown"  with  which  to  bewilder  our 
reasoning  faculties.  Is  the  "electricity  of  the  medium"  a 
new  entity  distinct  from  the  ether  ?  If  so,  is  it  a  fluid,  is  it 
of  a  material  nature,  is  it  force,  energy,  spirit,  demon,  or 
just  an  ordinary  scientific  term?  Whatever  it  is,  how  does 
it  attach  itself  to,  and  operate  in  or  upon,  the  medium? 
Does  it  affect  or  change  the  medium  in  any  manner  what- 
soever; and  if  so,  in  what  manner?  This  electricity,  this 
something,  is  assumed  to  be  so  related  to  the  medium  that 


SCIENTIFIC  THEISM  69 

it  can  be  displaced  toward  the  action  at  a  distance  effect. 
At  this  point  in  the  argument  the  scientific  magician  pro- 
duces from  his  resourceful  sleeve  another  entity  to  which 
he  gives  the  name  "action  at  a  distance  effect."  An  "effect" 
ordinarily  means  a  result  or  consequence  manifest  in  a 
change  of  state  or  condition  of  things.  Therefore,  in  the 
generally  accepted  meaning  of  the  term,  an  effect  certainly 
is  not  a  thing.  However,  if  an  effect  is  not  a  thing,  how  can 
we  comprehend  the  supposed  displacement  of  the  electricity 
of  the  medium  toward  this  effect?  Moreover,  this  "thing 
effect"  must  have  a  definite  spatial  position,  otherwise  how 
can  we  understand  the  displacement  of  another  something 
"toward"  it?  Furthermore,  the  "electricity  of  the  medium" 
must  itself  be  a  thing  if  human  intelligence  is  requested  even 
to  imagine  its  displacement.  Assuming,  then,  that  elec- 
tricity is  a  thing,  how  and  by  what  agency  is  it  propelled 
through  the  ether?  Does  it  pass  over  the  ether  particles 
as  a  ring  may  pass  along  a  wire?  Does  it  force  the  ether 
particles  to  open  a  free  path  for  it  along  the  line  of  its 
motion?  What  determines  the  direction  of  the  motion? 
When  it  reaches  its  goal  the  "thing  effect,"  how  does  it 
neutralize  to  a  great  extent  this  "thing  effect"?  Does  a 
battle  ensue  between  the  "thing  effect"  and  electricity,  after 
which,  and  when  the  smoke  has  cleared,  we  look  in  vain  for 
the  greater  portion  of  the  "thing  effect"  ?  Does  the  greater 
portion  of  the  "thing  effect"  go  up  in  smoke?  In  the  face 
of  all  these  unanswered  questions,  we  are  confronted  by 
the  statement  that  the  pressure  which  the  medium  exerts 
on  account  of  the  attraction  of  its  internal  electrifications 
tends  to  draw  the  bodies  together.  A  moment  ago  we 
beheld  the  spectacle  of  the  electricity  of  the  medium  being 
displaced  toward  the  action  at  a  distance  effect.  Now  we 
find  the  electrifications  performing  another  role  entirely. 
The  internal  electricities  are  now  acting  like  so  many  affini- 
ties under  the  spell  of  each  other's  mutual  attraction.  We 
infer  that  we  are  requested  to  complete  the  picture  by  con- 
ceiving the  next  tableau  as  revealing  the  electricities  in 
closer  proximity  to  each  other.  As  a  consequence  of  this 
action  of  the  electricities,  we  are  told  that  a  "pressure" 
arises  in  the  medium.  "Pressure"?  Is  that  a  new  term,  or 
is  it  a  condition?  Is  it  intended  by  this  new  term  that  we 


70  SCIENTIFIC  THEISM 

shall  conceive  a  condition  of  "compression"  as  arising  in 
the  medium?  Shall  we  think  of  the  ether  particles  as  being 
urged  into  a  smaller  space  by  the  similar  behavior  of  the 
electricities?  How  shall  we  reconcile  this  with  the  incom- 
pressibility  of  the  ether?  Will  a  vacuum  arise  in  the  rear 
and  front  of  the  compression  zone?  If  so,  what  about  the 
ether  as  an  all-pervading  continuum?  If  extraneous  ether 
particles  rush  in  to  fill  the  gap,  what  real  significance  can 
then  be  assigned  to  the  phenomena  of  compression?  The 
two  bodies  A  and  B  in  this  latter  event  will  have  no  induce- 
ment to  motion.  If  this  mere  phenomenon  of  compression 
is  a  sufficient  inducement  to  such  motion,  how  can  the  bodies 
move  with  these  extraneous  particles  of  ether  in  their  path 
of  progress  ?  If  a  vacuum  is  produced  in  the  rear  and  front 
of  the  compression  zone,  how  is  the  fact  that  a  state  of  com- 
pression exists  in  this  zone  to  be  made  known  across  a 
vacuum?  Assuming  that  the  opposite  electrifications  are 
displaced  toward  the  action  at  a  distance  effect  whose  nativ- 
ity seems  to  be  the  bodies  A  and  B,  and  supposing  that 
these  opposite  electrifications  are  things,  is  it  not  then  rea- 
sonable to  suppose  that  A  and  B  will  be  moved  farther 
apart?  The  fact  is  that  with  opposite  electricities  upon  A 
and  B,  the  bodies  tend  to  approach  each  other. 

Despite  all  these  pertinent  and  unanswered  inquiries, 
the  ether  advocate  shows  his  persistent  bias  for  his  favorite 
creature  by  charging  us  with  a  total  misunderstanding  of 
the  wonderful  real  relation  which  exists  between  ether  and 
matter.  We  are  consequently  informed  most  emphatically 
that  the  ether  permeates  matter  as  water  does  a  sponge — 
only  more  so,  of  course.  Moreover,  we  are  instructed  to 
conceive  the  body  A  as  a  hollow  ring,  whether  the  poor  thing 
A  can  obey  this  mandate  or  not;  similarly  our  omnipotent 
intellect  transforms  body  B  into  a  ring  with  its  inevitable 
hollow.  Now  intellectually  mold  the  ether  into  a  cylinder 
of  suitable  size  to  allow  the  rings  A  and  B  to  be  passed  over 
it.  Then  when  compression  sets  in  within  the  ether  cylinder 
the  bodies  A  and  B  simply  must  move  toward  each  other. 
Something  must  happen,  and  the  two  bodies  A  and  B  cer- 
tainly are  not  going  to  upset  all  respectable  traditions  and 
move  away  from  each  other.  If  the  bodies  A  and  B  are  to  be 
affected  at  all  by  the  state  of  compression  in  the  ether  cylin- 


SCIENTIFIC  THEISM  71 

der,  a  definite  causal  interaction  between  the  cylinder  and 
the  two  bodies  must  be  clearly  established. 

The  mere  fact  that  the  two  material  rings  A  and  B  are 
so  arranged  upon  the  cylinder  that  they  can  slide  upon  it  is 
not  a  sufficient  reason  for  the  assumption  that  such  a  sliding 
motion  will  be  initiated.  Moreover,  an  axial  contraction  or 
expansion  of  the  cylinder  is  not  a  sufficient  cause  for  a  dis- 
placement of  the  bodies.  It  is  readily  seen  that  the  cylin- 
drical model  can  be  sufficiently  modified  to  fulfil  the  require- 
ments imposed  by  those  who  emphasize  the  peculiar  impor- 
tance of  the  alleged  ability  of  the  ether  to  permeate  and 
invade  all  intra-molecular  spaces.  Such  an  extension  of  the 
idea  in  no  way  affects  the  crucial  point  in  the  argument, 
which  pertains  to  the  omission  of  that  fundamental  relation 
of  rapport  which  must  exist  between  the  ether  cylinder,  no 
matter  how  complex  the  model  is  made,  and  matter,  if  the 
latter  is  to  be  cognizant  of  any  modifications  within  the 
ether.  Even  the  entire  removal  of  the  ether  section  between 
A  and  B  cannot  disturb  the  peaceful  slumbers  of  these  two 
material  bodies. 

HYPOTHESIS  II 

First  Factor.  Action  at  a  distance  considered  as  non- 
existent. 

Second  Factor.  Entire  effect  regarded  as  existing  in  the 
ether. 

Assumptions 

In  Cases  I  and  II  of  the  first  hypothesis,  the  nature  of 
polarization,  represented  in  the  space  between  bodies  A 
and  B  in  Figures  1  and  2,  depends  upon  the  interpretation 
placed  upon  the  term  "electricity." 

In  the  second  hypothesis  the  symbolic,  graphical  repre- 
sentation is  intended  to  define  the  nature  of  an  electric 
charge  by  means  of  the  state  of  polarization  in  the  medium. 
The  particles  of  the  dielectric  are  considered  as  charged 
with  opposite  electricities.  No  action  at  a  distance  factor 
is  depicted  upon  bodies  A  and  B.  The  phenomenon  is  sup- 
posed to  be  due  entirely  to  the  activities  of  the  medium.  In  a 
space  C  devoid  of  the  medium  neither  forces  nor  polarization 


72 


SCIENTIFIC  THEISM 


are  considered  to  exist.  The  relations  are  shown  graphically 
in  Figure  3.    This  conception  of  the  ether  is  due  principally 


ETHER 


Figure  3 


to  Clerk-Maxwell,  who  desired  to  avoid  distance  forces  com- 
pletely. 

Implications 

The  bodies  A  and  B  are  regarded  as  contributing  nothing 
to  the  electric  disturbance  observed.  If  a  change  of  state 
in  the  system  is  observed,  we  have  at  least  the  right  to  ask 
for  a  physical  antecedent  in  the  event  that  the  term  "cause" 
is  deemed  objectionable.  Since  bodies  A  and  B  are  not 
included  in  the  series  as  factors  influencing  a  change  of  state 
in  the  system,  it  can  make  no  difference  in  the  condition  of 
the  system  if  a  charge  exists  upon  the  bodies,  or  if  the  notion 
of  a  charge  is  entirely  eliminated  from  consideration.  The 
fundamental  assumption  is  that  the  conditions  existing  in 
the  ether  are  independent  of  the  states  existing  upon  the 
bodies  A  and  B.  Nevertheless,  observable  physical  phe- 
nomena always  involve  material  aggregates,  in  the  absence 
of  which  physical  manifestations  become  impossible  for 
observation.  It  is  the  very  presence  of  a  charged  body 
that  constitutes  the  physical  antecedent  of  any  change  in 
condition  or  state  which  may  be  assumed  to  originate  in  the 
intervening  or  surrounding  space.  Without  the  existence 
of  this  charged  body,  the  entire  phenomenon  becomes  noth- 
ing but  a  dream  of  an  over-ardent  mathematician.  If  the 
charged  body  does  not  exist  or  perform  some  modifying 
function  in  the  system,  the  ether  space  must  remain  a  blank. 


SCIENTIFIC  THEISM  73 

The  introduction  of  a  charged  body  into  the  system,  never- 
theless, is  known  to  produce  a  change  of  state  in  the  system. 
This  change  of  state  may  not  be  a  new  condition  in  the  ether, 
but  it  is  a  genuine  modification  of  some  sort,  because  actual 
observations  testify  to  such  a  change.  Consequently  if  the 
ether  is  to  have  any  more  real  significance  than  empty 
space,  we  must  assume  that  the  condition  existing  upon 
the  charged  body  is  in  some  manner  transmitted  to  the 
ether.  The  advocates  of  this  latter  hypothesis,  no  doubt, 
find  considerable  solace  in  the  fact  that  the  ether  is  assumed 
to  be  so  intimately  interwoven  with,  or  contiguous  to,  the 
material  aggregate  that  no  empty  spaces  intervene  to  frus- 
trate or  hinder  action  or  transmitted  action  in  the  system. 
The  modern  physicist  fears  empty  space  as  persistently  as 
a  mouse  fears  a  cat.  Spatial  contact  is  the  "open  sesame" 
of  science.  Through  the  magic  of  this  relation  science  hopes 
to  give  plausibility  to  many  of  its  hypotheses.  Close  scrutiny 
of  the  notion  reveals  the  injection  into  it  of  an  activity 
principle  of  a  causal  nature,  capable  of  producing  real 
changes  and  modifications  in  relations  previously  existing. 
Spatial  contact  becomes  an  activity  factor  in  the  system. 
It  brings  about  the  transmission  of  an  influence  from  a 
group  a  to  another  physical  group  b.  Without  spatial  con- 
tact, the  scientist  believes  the  transmission  to  be  impossible. 
Consequently,  contact  is  the  factor  which  initiates  the  phe- 
nomenon of  transmission.  Therefore  it  must  be  regarded 
as  an  activity  factor  even  if  this  inference  is  objectionable 
to  science.  Nevertheless,  it  is  just  as  difficult  to  understand 
how  an  influence  can  be  transmitted  from  a  to  6  if  spatial 
contact  obtains  as  it  is  to  conceive  this  transmission  if  a 
vacuum  intervenes.  If  group  a  is  alien  to  group  b,  spatial 
contact  during  eons  of  time  will  not  cause  or  produce  a 
change  in  the  relation  of  a  to  b.  Spatial  contact  is  merely 
an  incident  of  physical  interaction.  It  may  be  an  inevitable 
incident,  nevertheless  it  is  not  an  active  factor  in  the  inter- 
action. It  "does  nothing,"  but  it  is  a  visible  relation  brought 
about  when  some  actual  change  has  taken  place  in  the  sys- 
tem. The  idea  of  action  at  a  distance  is,  therefore,  just  as 
conceivable  as  transmitted  action  by  means  of  spatial  con- 
tact. Neither  of  these  notions  is  tenable  unless  we  modify 
our  entire  conception  of  physical  action.  This  part  of  our 


74  SCIENTIFIC  THEISM 

discussion  will  be  considered  in  more  detail  hereafter.  For 
the  present  we  must  content  ourselves  with  the  statement, 
which  will  be  more  fully  proved  later  in  the  discussion,  that 
spatial  contact  is  not  an  adequate  bridge  between  matter 
and  ether.  It  is  evident  that  this  statement  obtains  also 
for  matter  aggregates.  If  a  charge  exists  upon  a  body,  then 
mere  spatial  contact  with  the  ether  will  not  cause  the 
medium  to  become  cognizant  of  this  fact.  Moreover,  we 
maintain  that  the  condition  of  the  body  is  a  factor  which 
cannot  be  ignored  in  a  consistent  interpretation  of  subse- 
quent events.  The  attempt  of  Maxwell  to  avoid  the  diffi- 
culties of  the  action  at  a  distance  hypothesis  has  only  re- 
sulted in  new  difficulties  of  just  as  serious  nature.  If  the 
reader  entertains  any  doubt  that  we  have  presented  the 
modern  ether  hypothesis  in  a  true  and  consistent  manner, 
we  refer  him  to  the  classic  memoir  of  Heinrich  Hertz. 

54.     Campbell's  Criticism  of  the  Ether. 

In  closing  this  portion  of  our  critical  analysis  of  the 
concepts  of  science,  we  shall  quote  the  following  from  Nor- 
man R.  Campbell's  work  "Modern  Electrical  Theory."  "The 
dictionary  may  be  searched  in  vain  for  a  word  which  has 
given  rise  to  more  confusions  and  misunderstandings;  the 
amazing  pronouncements  about  the  'sether'  which  have  been 
made  by  many  philosophers  are  rivalled  by  the  statements 
which  are  to  be  found  in  the  writings  of  men  of  science  of 
the  highest  repute.  There  seems  to  be  a  strange  attractive- 
ness about  the  word ;  a  student  never  feels  so  important  as 
when  he  is  about  to  introduce  it  into  his  examination  papers, 
it  is  to  be  found  in  monographs  on  the  geometrical  fourth 
dimension  and  in  treatises  on  the  more  obscure  issues  of 
theology.  .  .  .  Because  a  name  has  been  given  to  the 
conception  of  the  'sether/  it  has  been  assumed  straightway 
that  the  sether  is  a  substance,  separate  from  the  material 
bodies  of  the  system  and  moving  independently  of  them: 
for  no  other  reason  than  the  existence  of  the  name  it  has 
been  assumed  that  this  sether  has  mass,  elasticity,  even 
weight:  qualities  which  are  only  known  to  be  associated 
with  material  bodies  have  been  attributed  to  it,  one  after 
the  other,  until  Mendeleef  suggested  that  it  is  a  chemical 
element  with  a  place  in  the  periodic  series." 


SCIENTIFIC  THEISM  75 

55.  McDougall's  Mentiferous  Ether. 

It  is  indeed  gratifying  to  note  that  Campbell  advocates, 
in  the  above-cited  work,  the  abandonment  of  the  ether 
hypothesis.  It  is  a  regrettable  fact,  however,  that  Campbell, 
apparently,  adopts  the  Thomsonian  tube  of  force  as  a  sub- 
stitute for  the  ether  which  he  abandons.  In  thus  seizing 
another  inexplicable  convenience  unknown,  he  forcibly  illus- 
trates how  difficult  it  is  for  a  man  of  science  to  arrive  at  a 
consistent  philosophical  conception  of  the  universe.  As  a 
scientific  talisman  the  ether,  nevertheless,  remains  supreme 
in  the  annals  of  science. 

It  is  a  lamentable  fact  that  Professor  McDougall  has 
added  another  ether  to  the  mutitudinous  clan.  He  calls 
his  new  "creation"  the  "mentiferous  ether."  It  is  the  very- 
latest  thing  in  ethers.  This  mentiferous  ether  is  a  psychic 
ether  and  as  such  it  is  a  revelation  in  ultra-fashionable  ether 
styles.  He  gives  "weight"  to  the  concept  by  designating  it 
as  an  imponderable  substratum.  The  states  of  conscious- 
ness have  always  proved  to  be  an  irresponsible  contingent, 
difficult  to  hold  together.  As  a  psychical  glue,  the  manufac- 
turer claims  marvels  for  his  mentiferous  ether.  Its  adhesive 
properties  are  so  wonderful  that  one  state,  through  its  use, 
readily  recognizes  another  state  and  converses  with  it,  in 
addition  to  the  fact  that  it  is  forced  to  acknowledge  itself 
as  a  dweller  in  the  same  spiritual  soul  house  with  other  con- 
scious states,  all  of  which  are  owned  by  the  same  spiritual 
proprietor.  The  preceding  considerations  are  sufficient  to 
dispose  of  this  latest  scientific  phantom. 

56.  Physical  Action  at  a  Distance.     Coulomb's  Hypothesis. 
Having  disposed  of  the  tube  of  force  and  the  ether  as 

inconsistent  and  rationally  impossible  hypotheses,  we  shall 
now  lend  our  attention  to  the  analysis  of  the  physical  action 
at  a  distance  phenomenon. 

FIRST  HYPOTHESIS  COULOMB'S 

Assumptions 

If  a  body  A  (Fig  4)  exists  alone,  then  there  is  no  action 
at  a  distance  exerted.  The  appearance  of  force  presupposes 


76  SCIENTIFIC  THEISM 

the  presence  of  at  least  two  bodies  (Fig.  5).  The  nature 
of  this  force  may  be  one  of  attraction  or  repulsion,  as  in- 
dicated in  Fig.  5.  This  view  of  action  at  a  distance  was 
entertained  by  Coulomb. 


ATTRACTION  OR  REPULSION 
Figure  5 

It  is  not  our  intention  to  discuss  the  most  vital  difficulties 
involved  in  this  or  in  the  second  hypothesis  under  this  cap- 
tion, for  the  reason  that  due  consideration  will  be  given  to 
the  matter  later,  when  we  analyze  the  problem  of  physical 
action  in  general.  Here  we  merely  wish  to  call  attention  to 
the  principal  views  which  have  appeared  in  regard  to  dis- 
tance action.  The  implications  which  we  shall  consider  will 
be  only  those  which  are  at  once  apparent. 

Implications 

It  is  clear  that  Coulomb's  hypothesis  involves  a  dualism 
of  matter  and  force.  The  inherent  difficulties  of  this  posi- 
tion have  been  pointed  out  in  part  in  the  above.  It  is 
assumed  that  when  the  body  A  exists  alone  no  action  is 
exerted  and  force  does  not  make  itself  manifest.  The 
instant,  however,  that  a  second  body  B  is  introduced,  then 
the  force  appears  and  the  activity  appears  as  either  attrac- 
tion or  repulsion.  It  may  be  impertinent  to  ask  whence  does 
the  force  proceed  to  the  bodies  ?  How  does  it  make  its  pres- 
ence known  ?  Does  it  subdivide  itself  in  any  particular  man- 
ner ;  and,  if  so,  what  governs  the  relative  amount  of  the  sub- 
divisions? Do  the  subdivisions  attach  themselves  to  the 
bodies  A  and  B  ?  What  mechanism  is  used  in  effecting  this 
attachment?  How  are  the  relative  amounts  that  go  to  A 
and  B  determined?  Shall  we  assume  that  the  force  exists 
not  upon  the  bodies  A  and  B,  but  between  them?  If  the 
latter  be  true,  how  does  the  force  make  its  desires  effectively 


SCIENTIFIC  THEISM 


77 


felt  in  or  on  A  and  B  ?  What  determines  the  choice  of  attrac- 
tion or  repulsion  as  the  final  result  of  the  interview  between 
matter  and  force  ? 

The  enunciator  of  this  hypothesis  has  not  deviated  from 
the  customary  course  pursued  by  men  of  science,  and  conse- 
quently he  has  simply  ignored  these  questions,  if  they  ever 
occurred  to  him.  All  that  seems  necessary  for  the  produc- 
tion of  a  scientific  hypothesis  of  this  kind  is  to  write  names 
like  force,  bodies,  attractions,  repulsions,  and  action  at  a 
distance  upon  pieces  of  paper,  throw  them  together  in  a 
hat,  and  then  you  can  observe  the  genesis  of  a  scientific 
hypothesis.  When  we  deal  with  the  problem  of  physical 
action  we  shall  point  out  difficulties  which  inhere  in  all 
these  hypotheses. 

SECOND  HYPOTHESIS 

Assumptions 

This  hypothesis  supposes  that  every  individual  body  sends 
out  strivings  throughout  space.  The  single  body  A,  shown 

in  Fig  6,  radiates 
these  hopes  and  de- 
sires in  all  direc- 
tions into  every  im- 
aginable point  of 
space.  The  observer 
does  not  become  cog- 
nizant of  these  long- 
*—  ings  of  the  body  A 
until  a  second  body 
B  is  introduced  into 
the  scenario.  Then 
the  action  of  the 
drama  begins,  and 
something  happens 
to  which  mathemat- 
Figure  6  ics  can  be  applied. 

Implications 

If  things  are  regarded  as  independent  and  unrelated, 
then  the  assumptions  of  the  second  hypothesis  are  of  no 


78  SCIENTIFIC  THEISM 

avail  in  establishing  action,  whether  the  action  be  consid- 
ered as  taking  place  across  a  void  or  through  a  medium.  If 
the  strivings  radiated  by  the  body  A  are  to  produce  an  effect 
or  a  change  in  the  condition  of  body  B,  then  body  B  must, 
as  it  were,  understand  the  language  of  body  A.  In  the  phy- 
sical universe  an  "understanding"  is  impossible  between 
bodies  unless  interaction  in  a  unitary  system  is  admitted. 
Moreover,  a  possible  "understanding"  is  not  conceivable 
in  the  physical  world  unless  the  cosmic  relations  are 
grounded  in  a  Reality  capable  of  creating  a  rational  inter- 
acting unitary  world  order.  The  ordered  responsive  rela- 
tions between  things  in  this  unitary  cosmic  system  are  due, 
then,  to  an  omniscient  act  of  God.  The  cosmic  symphony 
is  God's  composition  and  its  harmonious  phrasing  of  inter- 
action is  due  to  His  Divine  Intelligence.  The  "understand- 
ing" between  things  is  that  God-given  endowment  which  we 
perceive  as  those  intelligible  rational  relations  which  we  call 
the  laws  of  nature's  interaction. 

57.     Interaction  According  to  Boscovich. 

We  believe  that  a  broad  interpretation  of  the  views  held 
by  Father  Boscovich,  and  enunciated  by  him  in  1750,  include 
interaction  between  his  force  centers  regarded  as  a  unitary 
system.  Father  Boscovich  realized  fully  that  action  at  a 
distance  is  involved  in  all  physical  phenomena.  He  showed 
profound  insight  in  his  unification  of  force  and  matter  in 
the  concept  of  the  force  center.  His  contention  that  these 
force  centers  exhibit  their  mutual  dependence  in  mutual 
attractions  and  repulsions  indicates  that  he  realized  the  futil- 
ity of  the  notion  that  the  centers  are  independent.  Accord- 
ing to  Boscovich  the  force  center  is  endowed  with  inertia. 
We  may  think  of  the  inertia  as  resistivity  to  a  change  in  the 
condition  of  motion.  Since  a  condition  of  absolute  rest  or 
zero  motion  is  unknown  in  the  physical  universe,  we  pro- 
vide in  the  Space-Time  Potential  for  this  resistivity  in  our 
gyrational  groups  of  force  centers.  The  basic  concepts  of 
the  Space-Time  Potential  are  modern  developments  of  the 
prophetic  insight  of  Father  Boscovich. 

In  the  following  we  shall  present  the  fundamental  facts 
underlying  physical  action. 


SCIENTIFIC  THEISM  79 

58.  The  Basic  Elements  of  the  Space-Time  Potential. 

The  following  principles  constitute  the  fundamental 
truths  which  serve  as  the  foundation  upon  which  the  purely 
physical  assumptions  rest: 

1.  The  existence  of  God. 

2.  All  reality  owes  its  existence  and  maintenance  to  God. 

3.  The  immanence  of  God  throughout  the  universe,  and 
also  His  transcendence. 

4.  The  cosmos  is  a  unitary,  interacting,  rational,  pur- 
posive, and  teleological  system. 

Auxiliary  Principles 

1.  Matter  is  composed  of  cosmic  activity  centers  mani- 
fest in  space  and  time  appearing  in  accordance  with  the  law 
of  causation.    Matter  owes  its  existence  to  a  creative  act  of 
God. 

2.  Action  at  a  distance  is  presupposed  in  all  physical 
action. 

3.  Independent  and  distinct  force  entities  do  not  exist 
apart  from  matter.    Kaufmann's  researches  bear  out  this 
contention. 

5.  The  continuance  of  cosmic  activity  involves  the  main- 
tenance of  an  ultimate  potential  difference.     God  only  is 
capable  of  maintaining  this  ultimate  potential  difference. 

The  cosmic  energy  owes  its  existence  to  a  creative  act 
of  God.  The  maintenance  of  that  ultimate  potential  differ- 
ence which  guarantees  the  continued  operation  of  the  cosmic 
machinery  is  due  to  the  immanence  of  God,  who  is  also 
transcendent.  The  Divine  Intelligence  is  not  only  immanent 
in  the  universe,  but  His  Being  is  also  transcendent. 

59.  Fundamental  Concepts. 

In  order  to  measure  and  record  the  magnitude  of  phy- 
sical change  it  is  necessary  arbitrarily  to  differentiate  phe- 
nomenal action  into  particularized  groups.  This  involves 
the  arbitrary  separation  of  a  given  phenomenon  into  phases 
interpretable  in  terms  of  arbitrary  concepts  capable  of 
mathematical  representation.  Unity  is  consequently  differ- 
entiated into  multiplicity,  which  has  no  significance  other 
than  an  arbitrary  and  necessary  convenience.  These  arbi- 


80  SCIENTIFIC  THEISM 

trary  conceptual  artifices  do  not  thereby  achieve  existence 
as  independent  physical  realities.  Therefore  there  ensues 
a  complete  relativity  of  those  basic  arbitrary  concepts  which 
constitute  the  alphabet  of  the  language  of  science.  This  very 
relativity  of  meaning  constitutes  the  closed  chain  of  the 
conceptual  edifice  of  science.  This  inherent  relativity  forces 
us  to  pass  beyond  the  closed  chain  if  we  wish  to  arrive  at  a 
real  understanding  of  physical  phenomena.  Within  the 
closed  chain  no  genuine  explanation  of  physical  change  is 
possible.  Every  explanation  within  the  closed  chain  is 
merely  relative.  One  fragmentary  action  is  explained  in 
terms  of  some  other  fragmentary  action.  One  concept 
involves  another,  and  so  on  for  ever  and  ever  around  the 
circle  of  concepts.  No  single  concept  is  independently 
defined.  By  remaining  within  the  closed  conceptual  chain 
we  cannot  arrive  at  an  independent  principle  capable  of 
explaining  physical  phenomena.  Thus  we  are  forced  out- 
side of  the  closed  chain  to  the  concept  of  God  as  the  only 
concept  which  can  account  for  physical  action. 

The  complete  relativity  is  another  proof  of  the  complete- 
ness of  the  world  within  itself.  It  is  a  proof  that  the  world 
is  a  unitary  interacting  system.  It  is  a  proof  that  the  world 
is  a  created  completeness  created  by  a  Being  distinct  from 
any  form  observed  within  the  system.  The  entire  structure 
of  science,  therefore,  becomes  a  proof  of  the  existence  of  God 
the  Creator.  Science  would  not  be  possible  without  concepts, 
but  a  colossal  error  is  committed  when  science  ascribes  more 
than  relative  significance  to  these  concepts.  Science  ex- 
tracts and  isolates  concepts  from  a  unitary  reality;  then 
these  mere  products  of  thought  are  endowed  by  science  with 
physical  reality.  A  physical  model  constructed  from  such 
concepts  must  always  remain  inoperative ;  the  parts  of  the 
machinery  may  be  properly  designed,  but  the  motive  power 
is  missing.  A  pure  mechanistic  theory  of  the  universe  is 
impossible. 

The  Space-Time  Potential  interprets  the  physical  world 
by  means  of  relative  concepts.  Its  physical  model  is  merely 
a  tentative  design  devised  for  the  sole  purpose  of  rendering 
the  cosmic  machine  more  intelligible  and  assisting  in  the 
further  and  more  perfect  elaboration  of  the  design.  The 
source  of  the  primal  motion  of  the  cosmic  machine  cannot 


SCIENTIFIC  THEISM  81 

be  found  in  any  of  its  members  nor  in  any  of  its  relative 
concepts.  No  physical  machine  is  operated  by  self -generated 
power.  Stevinus,  in  his  work  "Hypomnemata  Mathematica" 
(1605),  proved  by  means  of  a  closed  chain  and  the  inclined 
plane  over  which  it  was  suspended  that  perpetual  motion  is 
impossible.  The  cosmic  machine  is  no  exception  to  this 
scientific  proof.  Scientists  would  like  well  enough  to  make 
just  one  exception  in  favor  of  the  cosmic  machine.  Such 
an  exception  would  make  all  their  work  of  no  value.  Con- 
sequently primal  motion  is  due  to  an  agency  outside  of  the 
cosmic  machine.  Since  the  relativity  of  this  agency  pertains 
to  the  whole  cosmic  machine  and  is  not  involved  as  a  part 
thereof,  such  an  agency  is  efficacious  in  originating  primal 
motion.  The  concept  of  God  satisfies  this  demand. 

60.  The    Relative    Physical    Concepts    of    the    Space-Time 

Potential. 

The  relative  physical  concepts  of  the  Space-Time  Poten- 
tial contain  no  activity  principle  capable  of  accounting  for 
physical  phenomena.  This  activity  principle  is  found  in 
the  existence  of  God.  The  relative  concepts  are  epitomized 
relative  phases  of  genuine  physical  action.  They  are  only 
of  relative  value  in  describing  phases  of  phenomenal  action 
whose  ultimate  significance  cannot  be  defined  in  physical 
terms. 

61.  General  Relativities. 

Matter  and  Action 

Matter  is  known  only  through  physical  action. 
Physical  action  always  involves  matter. 

Action  and  Reaction 

To  every  action  there  is  opposed  an  equal  reaction. 
Consequently  every  physical  action  involves  two  mate- 
rial systems : 

1.  The  Excitant  System. 

2.  The  Concurrent  System. 

The  Excitant  System  is  that  system  which  we  arbitrarily 
select  as  the  initiatory  system  in  the  causal  nexus.  The 
Concurrent  System  is  that  system  which  responds  to  the 


82  SCIENTIFIC  THEISM 

initiatory  system  in  accordance  with  the  law  of  equality 
between  action  and  reaction.  Both  systems  are  material 
systems.  The  Concurrent  Material  System  may  in  certain 
class  phenomena  play  the  part  of  a  medium.  The  Concur- 
rent System,  when  regarded  as  a  medium,  does  not  thereby 
become  an  Ether,  because  the  Ether  is  not  a  material 
system.  On  the  contrary,  the  Concurrent  System,  being 
matter,  possesses  all  the  properties  of  matter,  and  its  con- 
tent contains  none  of  the  inconsistencies  of  an  ultra-material 
ether. 

Motion 

The  concept  of  motion  involves : 

1.  A  center  or  body  which  moves. 

2.  Another  center  or  body  in  respect  to  which  it  moves. 

3.  A  distance  traversed. 

4.  A  time  interval  consumed  in  the  displacement. 
Motion  may  be  described  as  being : 

1.  Rectilinear. 

2.  Curvilinear. 

3.  Combinational,  involving  rectilinear  and  curvilinear 
displacement. 

62.     Primary  Relativity  Concepts. 

Action  Phase 

Physical  action  always  means  interaction.  The  systems 
involved  in  interaction  exhibit  interdependent  physical 
changes.  For  the  purpose  of  analysis  we  arbitrarily  differ- 
entiate physical  change  or  action  into  such  convenient  con- 
ceptual types  as  mass,  velocity,  acceleration,  force,  torque, 
kinetic  reaction,  impulse,  work,  energy,  electric  charge, 
attraction,  repulsion,  equilibrium,  etc.  To  these  conceptual 
types  of  physical  change  we  given  the  name  action  phases. 
The  actual  physical  change  involves  many  action  phases. 
Action,  then,  is  a  continuous  characteristic  physical  unity 
which  involves  a  multiplicity  of  action  phases.  These  action 
phases  have  no  independent  reality.  They  are  not  indepen- 
dent physical  entities.  The  action  phases  are  convenient 
analytical  segregations  from  a  reality  whose  existence  in- 


SCIENTIFIC  THEISM  83 

volves  more  than  the  sum  total  of  these  thought  segrega- 
tions. 

Physical  Measurement 
All  physical  measurement  is  relative. 

Mass  Phase 

Mass  phase  is  one  of  many  action  phases  pertaining  to 
matter.  Formerly  mass  was  considered  to  be  that  property 
of  matter  which  served  best  to  represent  a  body  in  the  in- 
vestigation of  its  motion  because  it  was  intimately  con- 
nected with  motion,  and  also  for  the  reason  that  it  remained 
a  constant  throughout  motion.  For  ultra-atomic  particles 
this  is  no  longer  true  except  within  well-defined  limits.  For 
bodies,  however,  the  relation  holds.  The  relativity  of  mass 
was  established  by  Kaufmann,  who  showed  that  the  mass  of 
the  electron  varies  with  the  variation  in  velocity.  Ultimate 
matter  is,  therefore,  not  a  fixed,  unchanging  something.  We 
must  readjust  our  notion  of  mass  and  think  of  it  as  a  phase 
of  kinetic  matter.  From  this  new  viewpoint  we  define 
mass  phase  as  follows: 

Mass  phase  is  that  segregated  action  phase  of  kinetic 
matter  which  lends  continuity  to  physical  change. 

Measurement  of  Mass  Phase 

Let  Fl  and  F2  be  the  force  phases  involved  in  the  inter- 
action of  two  bodies  exhibiting  the  respective  mass  phases 
Afx  and  M,,  and  let  at  and  a2  be  the  corresponding  observed 
acceleration  phases  ;  then  the  following  relations  hold  : 


F2  =  M2.a2, 
Mi_Fi    a^ 

M2  ~  F2    ai 

The  latter  expression  points  to  two  methods  of  relatively 
measuring  mass  phases;  the  first  method  being  relative  to 
the  force  phases,  while  the  second  method  depends  for  its 
relativity  upon  the  acceleration  phases. 


84  SCIENTIFIC  THEISM 

METHOD  I.    FORCE  PHASES  USED  AS  THE  RELATIVE 
MEASURE  OF  MASS  PHASES 

It  is  evident  that  if  at  =  a2,  then  the  expression 

Mi    F!    a2 

^r-=r-  =  ^-  •  —         becomes 

M2    F2    at 

Mi    ft 

M2    F2' 

This  is  the  case  when  the  two  bodies  are  subjected  to  the 
common  acceleration  g  due  to  gravity.  In  that  case  the 
force  phases  F^  and  F2  become  the  corresponding  weight 
phases  W^  and  W2  and  we  have : 

Wi-Mi.g 

W2  =  M2.g,      and  consequently 
Mi  =  Wi 
M2     Wa' 

It  follows  that  we  have  a  relativity  equation  between  mass 
phases  and  force  or  weight  phases.  In  other  words,  the 
mass  phases  are  proportional  to  the  weight  phases.  We 
have  not  achieved  an  absolute  measure  of  the  mass  phase. 
The  method  is  purely  relative  because  the  weight  or  force 
phase  is  not  of  the  same  conceptual  order  as  the  mass  phase. 
Moreover,  the  fact  that  we  have  mathematically  eliminated 
the  common  constant  g  does  not  involve  the  actual  elimina- 
tion of  that  physical  activity  relation  upon  which  the 
acceleration  g  depends.  We  have  therefore  used  the  force 
phase  to  measure  the  relative  magnitude  of  the  mass  phase. 

METHOD  II.  ACCELERATION  PHASES  USED  AS  THE  RELATIVE 

MEASURE  OF  MASS  PHASES 
In  the  expression 

Mi_Fi   ajf 
M2~F2'a1' 

if  we  arrange  conditions  so  that  Fl  —  F2,  then 

MI       8,2 


SCIENTIFIC  THEISM  85 

In  this  case  the  mass  phases  will  be  inversely  proportional 
to  the  acceleration  phases.  This  latter  method  is  conse- 
quently no  more  absolute  than  the  former.  Hence  the  sec- 
ond method  is  merely  a  relative  measure  of  the  mass  phase. 

Mathematical  Definition  of  Mass  Phase 

The  mass  phase  M  of  a  body  is  that  relative  phase  magni- 
tude which  is  commensurate  with  the  quotient  obtained  by 
dividing  the  magnitude  of  the  force  phase  F  by  the  magni- 
tude of  the  acceleration  phase  a.  The  truth  of  this  defini- 
tion is  evident  from  the  following  relations : 


M .  a  =  M(  -£i ),  therefore 

F=_jF 
a     /dv 


Measurement  of  the  Magnitude  of  Motion. 

Velocity  Phase 

The  velocity  phase  is  a  mathematical  measure  of  motion. 
The  velocity  phase  v  involves  both  space  and  time  in  that  it 
is  defined  as  the  quotient  obtained  by  dividing  the  distance 
s  traversed  by  the  center  in  the  time  period  t  consumed  in 
the  displacement.  For  a  constant  velocity  the  requirement 
is  that  the  distance  traversed  in  equal  intervals  of  time, 
however  small  these  time  intervals  may  be,  shall  be  equal. 
The  general  expression  for  velocity  phase  v  is 

_s  _ds 
~t~dt* 

The  term  speed  is  used  to  denote  velocity  irrespective  of 
direction.  Motion  generally  involves  both  changes  in  velo- 
city and  direction,  hence  the  following  general  definition  of 
velocity  phase. 

The  velocity  phase  of  a  center  in  any  point  of  its  path  is 
the  quotient  obtained  by  dividing  the  immediately  adjoining 
distance  traversed  by  the  time  period  of  the  center  whose 
direction  is  regarded  as  the  instantaneous  tangent  to  the 
curve  of  its  path  of  motion.  Velocity  phase  is  purely  rela- 
tive and  involves  an  arbitrary  reference  point  or  reference 
system. 


86  SCIENTIFIC  THEISM 

Acceleration  Phase 

The  acceleration  phase  is  a  mathematical  measure  of  the 
change  of  the  rate  of  motion.  Like  the  velocity  phase,  it 
involves  space  and  time  and  is  always  a  relative  measure. 
It  involves  a  change  in  the  velocity  phase.  The  change  in 
the  velocity  may  involve  an  increase  or  a  decrease  (posi- 
tive or  negative  acceleration),  it  may  involve  a  change  in 
the  direction  of  the  motion,  and  it  may  involve  a  change  in 
the  velocity  as  well  as  in  the  direction. 

This  may  be  stated  mathematically  by  letting  vv  and  v^ 
be  the  respective  velocities  at  the  beginning  and  the  end  of 
a  time  period  t,  then  the  acceleration  a  is  given  by  the 
relation 

V2-V1 

a=~r 

The  general  definition  of  acceleration  may  be  formulated 
as  follows:  The  acceleration  phase  of  a  center  in  any 
point  of  its  path  is  the  quotient  obtained  by  dividing  the 
difference  in  the  velocities  dv  accruing  during  an  infini- 
tesimally  short  period  of  time  dt  by  this  time  period  dt.  The 
path  traversed  is  considered  of  infinitesimal  length.  The 
expression 


average  acceleration  or  rate  of  change  of  velocity. 
When  the  distance  traversed  becomes  infinitesimally 
short  then  (t>2-^i)  becomes  dv,  and  t  becomes  dt,  and  the 
general  definition,  stated  mathematically,  becomes 

dv 


Force  Phase 

Force  phase  is  that  segregated  action  phase  of  kinetic 
matter  which  qualifies  the  magnitude  of  the  intensity  of 
the  real  interaction  between  kinetic  matter  groups.  The 
actual  physical  change  is  not  brought  about  by  independent 
force  entities.  There  are  no  independent  force  entities. 
The  intensity  of  the  interaction,  however,  may  be  relatively 
measured  in  terms  of  force  phases. 


SCIENTIFIC  THEISM  87 

Mathematical  Definition  of  Force  Phase 
The  force  phase  F  is  that  relative  phase  magnitude  which 
is  commensurate  with  the  product  of  the  mass  phase  M 
and  the  acceleration  phase  a,  hence 


Kinetic  Reaction  Phase 

From  the  general  law  of  action  and  reaction  we  know 
that  to  every  action  there  is  opposed  an  equal  reaction. 
Consequently  the  sum  of  the  action  and  the  reaction  ex- 
hibited in  a  physical  change  is  equal  to  zero.  Now  if  we 
think  of  action  as  exhibiting  a  force  phase  and  reaction  as 
exhibiting  a  kinetic  reaction  phase,  then  we  may  state  the 
general  law  as  follows: 

The  sum  of  all  the  force  phases  exhibited  in  a  physical 
change  plus  the  kinetic  reaction  phase  equals  zero.  Stating 
this  mathematically,  we  have :  Sum  of  all  the  force  phases 
-j-  the  kinetic  reaction  phase  =  0 ;  or 

M.a.  +  Kinetic  reaction  phase  —  0 ;  hence 

M.a.  =  —  Kinetic  reaction  phase  =  —  M.a  =  —  F. 

The  general  expression  will  involve  a  constant  of  propor- 
tionality C.  This  constant  C,  however,  becomes  unity  when 
the  quantities  involved  in  the  expression  are  measured  in 
terms  of  the  same  units.  The  negative  sign  indicates  that 
the  kinetic  reaction  phase  R  is  opposed  to  the  force  phase  F. 

Mathematical  Definition  of  Kinetic  Reaction  Phase 
The  kinetic  reaction  phase  R  is  that  relative  phase  magni- 
tude which  is  commensurate  with  the  product  of  the  mass 
phase  M  and  the  acceleration  phase  a.  It  is  equal  in  magni- 
tude, but  opposed  to  the  force  phase  F.    Consequently, 

R=-F=-M.a=-M( -T7 


The   Three   Cosmic  Fundamentals 

The  conceptual  structure  of  the  physical  universe  is  built 

upon  the  three  fundamentals,  space,  time,  and  interaction. 

The  last,  i.  e.,  interaction,  involves  rational  causation  with 

its  inevitable  accompaniment  of  natural  laws.    The  causa- 


88  SCIENTIFIC  THEISM 

tion  is  both  primary  and  secondary.  The  interaction  in  the 
physical  universe  involves  a  manifold  of  secondary  causes. 
Since  the  system  is  complete  within  itself,  these  secondary 
causes  are  as  completely  relative  as  all  the  relativity  con- 
cepts. No  secondary  causation  within  the  system  can  ac- 
count for  its  initial  and  maintained  interaction.  The  uni- 
tary relativity  system  owes  its  existence  to  the  Being  of 
God.  The  three  cosmic  fundamentals  consequently  are 
space,  time,  and  potential. 

The  physical  tapestry  of  the  universe  is  a  web  woven 
from  the  woof  of  potential  and  the  warp  of  those  forms 
of  apprehension  which  we  call  space  and  time.  The  pri- 
mary relativity  concepts  are  built  upon  these  three  cosmic 
fundamentals. 

63.     Secondary   Relativity  Concepts. 

The  secondary  relativity  concepts  are  built  up  from  com- 
binations of  the  primary  relativity  concepts.  Consequently 
they  also  involve  the  three  cosmic  fundamentals  as  their 
basic  constituents.  Two  principal  conceptual  combinations 
may  be  made  from  the  force  phase  and  the  two  forms  of 
apprehension,  space  and  time. 

I.    THE  FORCE  PHASE  COUPLED  WITH  THE  TIME  FORM 

When  interaction  exhibits  a  displacement  of  a  center  or 
body,  then  the  action  intensity  may  be  considered  as  com- 
mensurate with  the  product  of  the  force  phase  and  the  time 
interval  involved  in  the  change. 

Mathematical  Definition  of  Impulse  Phase 

If  the  force  phase  is  constant  both  in  magnitude  and 
direction,  then  the  impulse  phase  7  is  commensurate  with 
the  product  of  the  force  phase  F  and  the  time  interval  t  of 
the  change.  Consequently  we  have  the  expression : 

I  =  F.t 

Now  if  the  force  phase  varies  in  magnitude  and  direc- 
tion, then  we  must  add,  by  the  calculus,  the  impulse  phase 


SCIENTIFIC  THEISM  89 

dl  exhibited  in  infinitesimal  intervals  of  time  dt.  Therefore 
the  expression  becomes 

dl  =  F .  dt,      and 

1=  /F.dt 

J  o 

II.  THE  FORCE  PHASE  COUPLED  WITH  THE  SPACE  FORM 
When  interaction  exhibits  a  displacement  of  a  center  or 
body,  then  the  action  intensity  may  be  considered  as  com- 
mensurate with  the  product  of  the  force  phase  and  the  dis- 
placement distance. 

Mathematical  Definition  of  Work  Phase 
If  the  force  phase  is  constant  both  in  magnitude  and 
direction,  then  the  work  phase  W  is  commensurate  with  the 
product  of  the  force  phase  F  and  the  distance  s  of  displace- 
ment.   Therefore  we  can  write  the  following  expression: 

W=F.s 

If  the  force  phase  varies  in  magnitude  and  direction,  then 
we  must  add,  by  the  calculus,  the  work  phases  dW  exhibited 
in  infinitesimal  distances  ds.  Therefore  the  following  ex- 
pression obtains ; 

=  F.ds,     and 

W  /F.ds 


r  /F. 

J  o 


Mathematical  Definition  of  Energy  Phase 
Energy  phase  and  work  phase  are  correlative  concepts. 
The  energy  phase  E  is  commensurate  with  the  work  phase 
W,  which  is  developed  during  a  change  from  an  actual  con- 
dition to  a  standard  condition.  The  inverse  process  in- 
volves the  same  work  phase  magnitude.  Consequently  the 
energy  phase  E  may  be  regarded  as  commensurate  with  the 
work  phase  W  which  must  be  expended  in  bringing  about  a 
change  from  a  standard  condition  to  an  actual  condition. 
Herein  we  clearly  see  the  ascending  and  the  descending  pro- 
cesses involved  in  a  change  from  a  condition  A  to  a  condi- 
tion B.  The  energy  phase,  or  the  work  phase  involved,  in 
passing  either  from  condition  A  to  condition  B,  or  from 


90  SCIENTIFIC  THEISM 

condition   B   to    condition   A,    is    in    either    case    of   the 
same  magnitude. 

The  manifesting  energy  phase  which  is  concomitant  with 
motion  is  called  kinetic  energy,  while  the  available  work 
phase  due  to  position  is  termed  potential  energy.  An 
available  work  phase  is  commensurate  with  a  potential  en- 
ergy phase,  while  a  developing  or  unfolding  work  phase  is 
commensurate  with  the  kinetic  energy  phase.  Ultimately  the 
various  forms  of  energy  phases  are,  in  the  last  analysis,  of 
a  kinetic  nature.  If  we  regard  the  matter  from  the  stand- 
point of  action  and  reaction,  then  the  kinetic  energy  phase 
E  is  commensurate  with  the  work  phase  W  involved  in  the 
production  of  a  velocity  phase  v  against  the  interacting 
kinetic  reaction  phase  R.  Stated  mathematically  this  rela- 
tion takes  the  form 


E 
since 


=-W=-  /  R.ds=-  /(-F)ds  =  -  /    j-M^ 

Jo  Jo  Jo 


-J-,  ds  =  v.dt,  and 
dtr 


E=-  /   |-M(^|v.dt  =  M  /v.dv  =  ^Mv2-^ 


In  the  above  the  first  negative  sign  signifies  that  an  energy 
phase  E  is  developing  as  a  v/ork  phase  W  against  the  kin- 
etic reaction  phase  R.  The  negative  sign  preceding  the 
term  F.ds  indicates  that  the  force  phase  appears  as  a  kin- 
etic reaction  phase. 

The  last  of  the  above  expressions, 


represents  the  change  in  the  kinetic  energy  phase 
which  is  concomitant  with  that  work  phase  which  is  in- 
volved in  the  change  of  the  velocity  from  v0  to  v. 

The  relativity  concepts  defined  above  constitute  the  basic 
concepts  from  which  all  other  necessary  concepts  may  be 
derived.  They  have  been  defined  as  phases  of  interaction 
having  no  independent  existence.  In  the  following  por- 
tions of  the  work  the  word  "phase"  has  been  omitted  for 
the  sake  of  brevity.  We  wish  to  emphasize  the  fact  that 


SCIENTIFIC  THEISM  91 

this  omission  in  no  way  alters  the  intent  of  the  definition 
given  above.  The  relativity  concepts  are  the  mathematical 
descriptions  of  arbitrarily  chosen  fragments  of  phenom- 
enal activity,  and  they  do  not  even  begin  to  exhaust  the 
content  and  meaning  of  reality,  which  is  known  in  its  full 
intent  only  to  God,  its  Creator. 

Interaction  in  a  Unitary  System 

Matter  is  that  persistent  phase  of  activity  which  ap- 
pears continuously  throughout  change  and  becoming.  Mat- 
ter has  persisted  in  its  continuous  and  uninterrupted  mani- 
festation throughout  the  ages.  This  persistence  in  the  past 
constitutes  our  only  basis  for  the  assumption  of  its  con- 
tinued manifestation  in  the  future.  We  cannot  prove  that 
this  assumption  Is  valid  indefinitely.  Ultimately  the  per- 
sistence depends  upon  teleology  above  finite  consciousness, 
that  is,  upon  the  omniscience  and  omnipotence  of  God. 
Phenomenally,  matter  is  differentiated  into  a  multiplicity 
of  interacting  and  related  activity  centers.  We  have  given 
the  name  monon  to  these  activity  centers.  Regarding  them 
from  their  force  phase  standpoint,  we  think  of  them  as 
force  centers.  Since  the  energy  phase  may  be  considered 
as  more  inclusive,  we  may  think  of  them  as  centers  of 
energy.  These  phases  are  not  invariable.  Their  only  con- 
stancy is  persistency  and  continuity.  This  is  true  of  the 
mass  phase  as  well  of  all  other  action  phases.  Through- 
out a  series  of  energy  transformations  in  a  given  system 
there  is  no  apparent  evidence  of  a  lose  or  gain  of  either 
mass,  force,  or  energy,  provided  that  we  make  the  system 
sufficiently  inclusive.  This  fact  serves  as  the  basis  of  the 
postulate  of  conservation.  This  persistency,  which  we  call 
conservation,  depends  for  its  future  continuation  upon  the 
life  of  God.  Action  phases  do  not  exist  as  independent 
entities.  Mass,  force,  and  energy  entities  do  not  exist  as 
independent  existencies.  Mass,  force,  and  energy  are 
phases  of  an  activity  which  includes  them  and  all  other 
action  phases.  Modern  scientific  research  bears  out  these 
contentions.  The  cosmos  is  a  unitary  interacting  system 
in  which  the  distance  and  duration  are  respectively  the 
spatial  and  temporal  indicators  of  the  relative  magnitude 
of  the  interaction  between  things. 


CHAPTER  IV 
THE  PROBLEM  OF  A  PHYSICAL  SUBSTRATUM 

64.     Physical  Substratum. 

CASE  I.    SUBSTRATUM  DEVOID  OF  QUALITIES 

Contemplation  of  the  world  of  phenomena  leads  us  to 
the  two  fundamental  concepts,  Being  and  Becoming.  In 
the  last  stage  of  every  analysis  of  the  nature  of  the  objects 
of  perception  we  encounter  some  type  of  elementary  par- 
ticles which  we  name  molecules,  atoms,  and  electrons.  Our 
question  concerning  the  nature  of  an  object  finally  resolves 
itself  into  the  discovery  of  the  kind  of  elements  of  which 
its  material  portion  is  made.  It  is  a  process  of  reducing 
complexity  to  simplicity. 

Let  us  take  for  consideration  the  well-known  substance 
water.  At  ordinary  temperatures  water  is  a  liquid,  at 
higher  temperatures  it  is  a  vapor,  and  at  lower  temperatures 
it  is  a  solid.  What,  then,  is  water  when  it  is  not  influenced 
by  temperature  or  other  conditions?  You  will  undoubtedly 
answer  this  question  by  saying  that  water  is  an  existent 
something  which  under  one  condition  reveals  itself  to  sense 
as  something  A,  while  it  appears  as  something  B  under 
another  condition,  and  under  a  third  condition  it  exhibits 
itself  as  something  C.  Experience  has  taught  us  that  a  sec- 
ond assumption  is  within  the  realm  of  the  highly  probable. 
This  is  the  assumption  that  a  reversal  of  the  order  of  the 
conditions  produces  a  reversal  in  the  appearance  of  the 
states  from  the  sequence  A,  B,  C,  to  C,  B,  A,  without  the 
anomalous  appearance  of  an  alien  state  M  totally  foreign 
to  the  substance  water.  A  thing,  then,  is  what  it  is  on 
account  of  the  regularity  of  its  changes  within  a  given 
series.  Independent  of  the  assumed  forms  within  the  series, 
a  thing  has  no  existence  independent  of  these  forms.  How- 
ever, you  will  maintain  that  the  crux  of  the  matter  lies  in 
the  fact  that  this  independent  existence  is  the  basic  sub- 

92 


SCIENTIFIC  THEISM 


93 


stratum  about  which  states  and  forms  drape  themselves. 
You  believe  that  the  existent  is  truly  represented  schemati- 
cally in  Figure  7,  where  a  real  substratum  A  is  vitally  associ- 

Ai  Aa  A» 


I 

p  •     Solid 

Liquid     — 

Gaseous 

Having 

The  Real  Substratum 
Void  of  Qualities, 
power  of  making  states  or 
qualities  appear. 

STATES  OK 
QUALITIES. 


Figure  7 

ated  with  the  states  A19  A2,  and  A8,  which  are  its  individual 
and  personal  property.  Your  contention,  then,  is  that  the 
real  substratum  A  is  the  abiding  essence  of  a  thing,  and 
that  the  A  is  the  subject  which  is  potent  to  give  reality  to 
the  changing  qualities  and  states  which  it  owns  in  a  manner 
analogous  to  the  varying  states  of  consciousness  which  you 
own  as  an  individual  ego.  These  arguments  remind  us  of 
Berkeley's  presentation  in  the  "Principles  of  Human 
Knowledge,"  from  which  we  quote  the  following: 

"But,  say  you,  though  it  be  granted  that  there  is  no 
thoughtless  support  of  extension,  and  the  other  qualities 
or  accidents  which  we  perceive :  yet  there  may,  perhaps,  be 
some  inert  unperceiving  substance,  or  substratum  of  some 
other  qualities,  as  incomprehensible  to  us  as  colours  are  to 
a  man  born  blind,  because  we  have  not  a  sense  adapted  to 
them.  But  if  we  had  a  new  sense,  we  should  possibly  no 
more  doubt  of  their  existence,  than  a  blind  man  made  to  see 
does  of  the  existence  of  light  and  colours.  I  answer,  first, 
if  what  you  mean  by  the  word  matter  be  only  the  unknown 
support  of  unknown  qualities,  it  is  no  matter  whether  there 
is  such  a  thing  or  not,  since  it  no  way  concerns  us:  and  I 
do  not  see  the  advantage  there  is  in  disputing  about  we 
know  not  what,  and  we  know  not  why."1 


1  Principles  of  Human  Knowledge,  Part  I,  Ixxvii. 


94  SCIENTIFIC  THEISM 

In  the  final  analysis,  then,  you  reduce  substratum  to  a 
material  of  reality.  It  is  neither  this  nor  that,  but  a  real, 
pure,  and  simple  basis  of  this  and  that.  In  short,  it  is 
naught  but  the  principle  of  reality. 

Objection  to  Case  I 

How  can  an  indeterminate,  independent,  and  empty 
substratum  A  show  preference  at  any  one  time  for  o^  as 
against  a2  or  a3  ?  By  a  process  of  successive  negation,  the 
"unknown  support"  of  states  and  qualities,  the  ultimate 
material  essence  or  substratum  is  reduced  to  an  empty  void. 
Let  us  quote  again  from  Berkeley,  in  the  Second  Dialogue 
between  Philonous  and  Hylas: 

"Phil.  Continue,  good  Hylas,  to  act  the  same  ingenuous 
part,  and  tell  me  sincerely  whether  you  can  frame  a  distinct 
idea  of  entity  in  general,  prescinded  from  and  exclusive  of 
all  thinking  and  corporeal  beings,  all  particular  things 
whatsoever. 

"Hyl.  Hold,  let  me  think  a  little.  I  profess,  Philonous, 
I  do  not  find  that  I  can.  At  first  glance  me  thought  I  had 
some  dilute  and  airy  notion  of  pure  entity  in  abstract;  but 
upon  closer  attention  it  hath  quite  vanished  out  of  sight. 
The  more  I  think  on  it,  the  more  am  I  confirmed  in  my 
prudent  resolution  of  giving  none  but  negative  answers,  and 
not  pretending  to  the  least  degree  of  any  positive  knowledge 
or  conception  of  matter,  its  where,  its  how,  its  entity,  or 
anything  belonging  to  it. 

"Phil.  When,  therefore,  you  speak  of  the  existence  of 
matter,  you  have  not  any  notion  in  your  mind. 

"Hyl.   None  at  all. 

"Phil.  Pray  tell  me  if  the  case  stands  not  thus :  at  first, 
from  a  belief  of  material  substance  you  would  have  it  that 
the  immediate  objects  existed  without  the  mind;  then  that 
their  archetypes ;  then  causes ;  next  instruments ;  then  occa- 
sions ;  lastly,  something  in  general,  which  being  interpreted 
proves  nothing.  So  matter  comes  to  nothing.  What  think 
you,  Hylas?  Is  not  this  a  fair  summary  of  your  whole 
proceeding?"1 


'The  Second  Dialogue,  pp.  257,  258. 


SCIENTIFIC  THEISM 
65.     Physical  Substratum. 


95 


CASE  II.    SUBSTRATUM  ASSUMED  TO  POSSESS  POWER  OP 
SELECTION  AND  ATTRACTION 

We  present  this  case  schematically  in  Fig.  8.  The  adher- 
ents to  this  view  think  of  the  states  and  qualities  as  inde- 
pendent entities.  They  assign  to  the  real  substratum  two 


INDEPENDENT 
STATES  OR 
QUALITIES. 

-  •     Solid 

The  Real   Substratum. 
Power  of  Selection  and  Attraction. 


A. 


Figure  8 

fundamental  properties  of  selection  and  attraction  by  which 
the  substratum  A  takes  unto  itself  a  particular  state,  for 
instance,  the  solid  state  o^  shown  in  the  scheme  of  Fig.  8. 

Objections  to  Case  II 

First.  How  shall  we  explain  the  mechanism  by  which 
the  real  A  selects,  attracts,  and  incorporates  with  itself  the 
state  (&!,  in  preference  to  another  state  bi  from  another 
series  of  states  or  qualities? 

Second.  As  far  as  phenomena  are  concerned,  indepen- 
dent states  and  qualities  give  us  all  we  need.  A  hypothetical 
substratum  merely  complicates  the  issue  without  in  any 
way  explaining  the  effects  observed  by  the  senses. 

In  trying  to  create  this  independent  substratum  in  a 
world  beyond  states  and  qualities  we  commit  the  same  error 
as  the  person  who  ascribes  the  color  of  a  body  to  the  body 


96 


SCIENTIFIC  THEISM 


beneath  the  pigment  which  was  applied  to  produce  the  par- 
ticular color.  The  pigment  does  not  communicate  its  color 
to  the  entire  substance  beneath  it.  The  body  does  not  select 
nor  attract  a  particular  pigment  in  preference  to  any  other. 
We  are  forced  to  the  conclusion  that  the  quality  of  color  is 
a  part  of  the  nature  of  the  pigment  and  not  of  the  body 
beneath  it.  You  will  retort  that  we  are  begging  the  ques- 
tion because  it  is  the  substratum  of  the  pigment  which  is 
responsible  for  its  color.  We  reply  that  the  process  by  which 
the  pigment  selects  from  the  cosmic  warehouse  a  preferred 
color  is  inconceivable,  and  we  reiterate  that  our  objections 
are  valid. 

66.     Physical  Substratum. 

CASE  III.    FIXEDNESS  GIVEN  TO  STATES  AND  QUALITIES  BY 

INJECTION  OF  A  GRAIN  OF  REALITY  INTO  A  THING 

The  desire  to  give  permanence  and  fixedness  to  the  states 

and  qualities  of  a  thing  is  the  root  of  a  notion,  held  by  many, 

that  a  portion  of  the  stuff  of  reality  is  injected  into  a  thing 

(see  Fig.  9).    This  stuff  of  reality  is  the  common  basis  or 

property  of  things,  and  when 
qualities  and  states  are 
grouped  about  it  we  have  ob- 
jects and  things  of  the  phe- 
nomenal world.  In  this  stuff 
of  reality  we  have  something 
akin  to  the  noumenon,  or 
thing-in-itself,  of  Kant.  Of 
the  thing-in-itself  Kant  says: 
"We  know  only  experiences, 
but  not  things-in-themselves." 
Nevertheless,  Kant  himself 
regards  the  thing-in-itself  as 
the  cause  of  phenomena  in  re- 
gard to  both  their  form  and 
matter.  In  this  respect  Kant 
involves  himself  in  a  serious 


SOLIDITY,  COLOR,  ETC. 
Figure  9 


self-contradiction,  for  in  so  far  as  he  has  limited  the  con- 
cept of  causality  to  experience,  the  realm  wherein  the 
thing-in-itself  is  unknown,  how,  then,  can  the  thing-in-itself 


SCIENTIFIC  THEISM  97; 

be  the  cause  of  phenomena?  Schopenhauer  believed  that 
he  unveiled  the  thing-in-itself  in  his  emphasis  of  the  will  as 
the  primary  phenomenon,  that  which  constitutes  the  very 
basic  essence  of  our  real  nature.  However,  since  all  we 
know  of  volition  is  phenomenal,  Schopenhauer's  principle 
of  sufficient  reason,  which  applies  to  phenomena,  leaves 
the  thing-in-itself  undiscovered.  We  quote  the  following 
from  Schopenhauer :  "That  what  Kant  opposed  as  thing-in- 
itself  to  mere  phenomenon — called  more  decidedly  by  me 
representation — and  what  he  held  to  be  absolutely  unknow- 
able, that  this  thing-in-itself,  this  substratum  of  all  phe- 
nomena, and  therefore  of  the  whole  of  Nature,  is  nothing 
but  what  we  know  directly  and  intimately,  and  find  within 
ourselves  as  the  will." 

"The  general  meaning  of  the  Principle  of  Sufficient 
Reason  may,  in  the  main,  be  brought  back  to  us:  that 
everything  existing,  no  matter  when  or  where,  exists  by 
reason  of  something  else.  Now,  the  Principle  of  Sufficient 
Reason  is  nevertheless  a  priori  in  all  its  forms:  that  is,  it 
has  its  root  in  our  intellect,  therefore  it  must  not  be  applied 
to  the  totality  of  existent  things,  the  Universe,  including 
that  intellect  in  which  it  presents  itself.  For  a  world  like 
this,  which  presents  itself  in  virtue  of  a  priori  forms,  is 
just  on  that  account  mere  phenomenon :  consequently,  that 
which  holds  good  with  reference  to  it  as  the  result  of  these 
forms,  cannot  be  applied  to  the  world  itself,  i.e.,  to  the  thing- 
in-itself,  representing  itself  in  that  world." 

We  see,  then,  that  both  Kant  and  Schopenhauer,  in  their 
sharp  distinction  between  noumenon  and  phenomenon,  in- 
ject into  the  world  an  antithesis,  indefensible  because  the 
distinction,  a  mere  product  of  the  intellect,  lacks  confirma- 
tion in  the  groundwork  of  reality. 

Objections  to  Case  III 

The  error  lies  in  postulating  two  separate  and  distinct 
entities  in  the  groundwork  of  reality :  first,  a  thing,  and  sec- 
ond, its  content ;  first,  a  substratum,  and  second,  its  qualities 
and  states;  first,  a  thing-in-itself,  and  second,  phenomena. 
A  grain  of  the  real  can  no  more  convey  reality  to  the  diverse 
qualities  associated  with  it  than  a  pigment  can  convey  its 
coloring  to  an  object.  It  is  futile  to  expect  that  a  sub- 


98 


SCIENTIFIC  THEISM 


- 

Sc 

>li 

d 

•     Liquid.    — 

Gaseous 

stratum  void  of  any  content  whatsoever  can  produce  from 
its  fatuous  depths  real  states  and  qualities.  Things  are  not 
real  because  of  the  presence  of  a  real  in  them.  Things  do 
not  become  real  because  a  real  is  injected  into  them,  but  they 
are  real  because  they  are  capable  of  displaying,  and  actually 
do  display,  that  type  of  activity  which  we  term  reality. 

67.     Identity  of  the  Real  with  the  States  and  Qualities. 

CASE  IV.    THE  HYPOTHESIS  OF  INTERACTION 
We  show  this  case  schematically  in  Fig.  10.    The  diffi- 
culties involved  in  the  previous  cases  are  due  to  a  search 

for  the  thing-in-itself 
beyond  itself,  to  the 
separation  in  thought 
of  thing  and  content. 
By  admitting  that  a 
thing  and  its  content 
Fisure  10  are  one,  that  qualities, 

states,  and  substratum  are  inseparable  real  unities,  we  avoid 
the  difficulty.  This  is  the  fundamental  tenet  of  the  hypoth- 
esis of  interaction  which  we  adopt  as  the  only  solution  of 
the  problems  reviewed  above.  We  have  referred  to  the  per- 
sistence of  the  sequence  in  change.  The  change  series  A,  B,  C 
can  be  and  is  reversed  by  a  reversal  of  the  antecedent  con- 
ditions. This  permanence  in  the  order  of  change  consti- 
tutes the  so-called  laws  of  action  of  things.  We  cannot 
separate  these  laws  from  things  with  any  more  justice  than 
we  can  think  into  the  real  a  substratum  beyond  the  real. 
Laws  are  not  entities  disparate  from  things;  they  are  not 
external  powers  which  influence  from  without  the  sequence 
in  the  activity  of  things.  The  separation  of  law  and  thing 
is  the  work  of  thought.  The  real  knows  no  such  separation. 
When  the  eternally  real  expresses  its  own  nature,  then 
thought,  finding  permanence  in  this  ever  changing  thing, 
describes  the  persistence  in  the  mode  of  behavior  of  things 
by  postulating  laws  which  hold  dominion  over  the  action  of 
things.  It  is  just  as  impossible  to  conceive  and  arrange  an 
effective  and  operative  understanding  between  laws  and 
things  regarded  as  separate  entities  as  it  is  similarly  to  con- 
nect substratum  and  states  considered  as  independent  exist- 


SCIENTIFIC  THEISM  99 

ences.  In  this  more  complete  view  of  activity  we  therefore 
maintain  the  identity  of  content,  law,  and  thing. 

Change  or  becoming,  exemplified  in  birth  and  death,  in 
origination  and  decay,  is  the  content  of  all  perceptual  knowl- 
edge. As  Heracleitus,  the  Greek  philosopher,  pointed  out, 
the  phenomenal  world  is  in  a  constant  state  of  flux  or  becom- 
ing. The  concept  of  being,  opposed  to  that  of  becoming, 
owes  its  origin  to  the  hope  of  finding  persistence  and  per- 
manency in  change  or  becoming.  Observed  phenomena  tell 
a  different  legend  to  us  than  can  be  consistently  brought 
forth  by  maintaining  that  an  empty  and  void  substratum  is 
an  effective  basis  of  things.  Things  are,  not  by  virtue  of  a 
substratum  or  ultimate  substance  in  them,  but  they  are, 
because  their  very  nature  makes  it  possible  for  them  to 
convey  to  us  the  notion  of  persistence  and  permanence.  This 
stability  and  permanence  in  things  gave  rise  to  the  notion 
of  a  rigid,  immutable  nucleus  or  substance  as  the  basic  root 
of  things.  The  prevalent  notion  of  becoming  or  change  is 
that  the  new  real  is  merely  a  continuation  of  a  previous  real. 
The  concept  of  a  coming  into  or  origination  of  a  new  real 
involves  the  notion  that  reality  arises  from  a  total  absence 
of  the  real.  Many  superficial  subterfuges  have  been  resorted 
to  in  order  to  avoid  this  implication. 

It  is  true  that  the  old  real  does  not  contain  within  itself 
the  reality  of  the  new.  The  old  reality  must  be  disposed  of 
before  the  advent  of  the  new  real.  A  reality  A  will  never 
cease  to  be  identically  equal  to  A  until  it  ceases  to  exist.  To 
originate  and  to  pass  away  is  a  continuous  process  during 
which  we  can  say  that  origination  equals  origination  and 
passing  away  equals  passing  away.  In  other  words,  A=A 
only  while  A  endures  precisely  as  it  is.  This  is  the  only 
sense  in  which  we  can  conceive  the  validity  of  the  Law  of 
Identity. 

Should  we  demand  the  indestructibility  of  things  as  a 
consequence  of  the  Law  of  Identity,  we  must  also  demand 
the  immutability  of  all  states,  qualities,  and  relations  which 
pertain  to  things.  There  would  then  be  no  phenomenal 
world.  The  notion  of  the  continuation  of  the  same  real 
unchanged  is  not  a  valid  one  in  view  of  the  facts  of  the 
phenomenal  world.  Permanence,  therefore,  is  to  be  found 
only  in  the  sameness  of  the  process  of  decay  and  becoming. 


100  SCIENTIFIC  THEISM 

Change,  then,  is  not  a  succession  of  self-contained,  immut- 
able reals  A,  B,  C  separated  as  entities  distinct  from  each 
other.  The  reals  A,  B,  C  cannot  exist  during  the  most  mi- 
nute interval  of  time  in  a  condition  of  rest.  The  realities 
A,  B,  and  C  cannot  at  any  stage  of  the  phenomenon  of 
becoming  be  regarded  as  stationary  independent  beings. 
Every  form  of  the  real  must  mean  that  the  phase  A  is  as 
truly  in  continuous  motion  as  any  other  phase  of  B  or  C. 
Moreover,  the  direction  in  which  becoming  advances,  the 
particular  sequence  in  which  change  takes  place,  must  be 
inherent  in  the  very  nature  of  the  thing  to  which  reality  is 
assigned.  Laws  external  to  reality  are  both  superfluous 
and  inoperative.  Being,  then,  is  not  a  passive,  inert  some- 
thing, but  it  is  energy  continuous  in  its  manifestation,  activ- 
ity permanent  as  the  basic  function  of  things.  Continuous 
life  and  activity  is  what  constitutes  reality. 

These  conclusions  may  remind  you  of  the  fundamental 
principles  of  Spinoza's  philosophy.  Far  from  denying  this, 
we  admit  that  we  are  at  one  with  him  if  you  will  do  him 
the  justice  of  seeking  for  the  basic  thought  which  forms  the 
nucleus  of  his  reasoning.  The  method,  however,  by  which 
Spinoza  attacked  his  problem  inevitably  led  him  into  diffi- 
culties in  the  rational  development  of  his  system  which 
obscured  the  great  truths  which  he  announced.  Spinoza 
says:  "I  understand  Substance  (substantia)  to  be  that 
which  is  in  itself  and  is  conceived  through  itself:  I  mean 
that  the  conception  of  which  does  not  depend  on  the  con- 
ception of  another  thing  from  which  it  must  be  formed. 
An  attribute  I  understand  to  be  that  which  the  intellect  per- 
ceives as  constituting  the  essence  of  a  substance."  For 
Spinoza  the  end  of  all  thought  is  found  in  the  principle  of 
uniformity  of  Nature.  Substance  and  law  are,  for  him,  iden- 
tical. Spinoza's  method  consists  in  deriving  ultimate  con- 
cepts by  a  process  of  elimination  of  the  limitations  imposed 
by  the  specific  qualities  observed  in  connection  with  the  ob- 
jects and  things  of  the  phenomenal  world.  A  concept  derived 
by  this  method,  from  which  every  semblance  of  the  reality 
of  phenomena  has  been  ejected,  is  nothing  save  a  name 
applied  to  an  empty  void  denuded  of  content.  Hegel  justly 
criticized  Spinoza's  Absolute  by  saying  that  it  is  like  unto 
the  lion's  den  to  which  all  tracks  lead,  and  from  which  none 


SCIENTIFIC  THEISM  101 

return.  Spinoza  creates  a  gulf  between  the  world  of  reality 
and  the  world  of  phenomena,  and  his  method  is  not  able 
to  provide  a  bridge  over  the  chasm.  In  fact,  no  system 
which  makes  this  distinction  between  appearance  and  reality 
can  ever  construct  a  rational  connecting  span  between  these 
worlds.  His  method  prevents  him  from  consistently  and 
rationally  reaching  the  ever  more  inclusive  reality  of  the 
unitary  interacting  universe  in  which  lesser  realities  find 
their  life's  consummation.  Notwithstanding  the  shortcom- 
ings of  his  method,  Spinoza  realized — shall  we  say  intui- 
tively ? — the  unitary  intimacy  of  substance,  nature,  and  law, 
for  he  does  point  out  that  nature  is  the  inherent  energy, 
active  and  manifest  in  all  that  exists;  it  is  "natura  natu- 
rans,"  and  not  merely  the  sum  of  all  that  exists,  "natura 
naturata." 

Again  we  call  attention  to  the  fact  that  we  do  not  agree 
with  philosophers  who,  like  Kant,  separate  reality  into  two 
distinct  parts,  noumena  and  phenomena.  Reality  is  not  a 
synthesis  of  two  entities,  a  thing-in-itself  and  its  phenom- 
enal aspects.  If  reality  is  a  synthesis  of  two  distinct 
essences,  then  we  must  assign  separate  properties  to  each 
of  the  two  types.  This  would  force  us  to  separate  the  man- 
ner of  knowing  and  perceiving  into  two  modes  correspond- 
ing with  the  two  types  of  entities.  The  procedure  may 
involve  us  in  the  conclusion  that  one  type  of  reality  is  un- 
knowable and  the  other  knowable.  For  this  and  other  rea- 
sons previously  stated  we  hold  the  view  that  the  substratum 
states,  qualities,  and  laws  are  not  independent  entities,  but 
that  a  unitary  and  not  a  synthetic  reality  manifests  its 
nature  phenomenally  to  sense.  In  maintaining  the  identity 
of  substratum  and  content  it  must  not  be  inferred  that  we 
hold  the  non-existence  of  either.  Reality  is  more  than  that 
which  is  given  by  sense  perception.  The  reality  of  a  thing 
proceeds  from  a  source  more  potent  than  mere  sense  mani- 
festation. The  mere  isolated  and  individual  data  furnished 
by  sense  perception  do  not  exhaust  the  significance  of  real- 
ity. The  soul  is  more  than  thought,  which  in  its  turn  is 
more  than  a  mere  sense  stimulation.  Nevertheless,  the  soul 
is  a  unitary  being.  A  thing  pulsates  and  throbs  with  a 
reality  greater  than  the  mere  kinetic  content  of  the  "now." 
Its  potential  content  of  the  "then"  indicates  a  reality  sus- 


102 


SCIENTIFIC  THEISM 


tained  and  potentially  assured,  which  appears  as  the  con- 
tentless  background  of  the  content  of  the  "now"  and  also 
as  the  potent  generative  background  of  the  content  of  the 
"then."  Thus,  in  thought,  is  substance  sundered  from  its 
content  because  the  present  content  does  not  exhaust  the 
total  reality  of  a  thing.  That  phase  of  reality  which  assures 
continuity  throughout  change  and  relative  permanence  to 
individuality  and  discreteness  constitutes  the  essense  of  sub- 
stance. Far  from  being  a  mere  product  of  thought,  sub- 
stance finds  its  significance  in  the  very  depths  of  reality. 
The  permanence  of  which  we  speak  points  to  the  maintain- 
ing potentiality  of  God.  Thus  we  are  in  accord  with  the 
intent  of  Scholasticism  in  its  treatment  of  the  relation 
between  substance  and  the  sensible  accidents  of  forms,  quali- 
ties, and  states. 

68.  The  Problem  of  Physical  Action. 

Thesis 

If  we  assume  the  independence  of  separate  and  distinct 
things,  actions,  states  or  forces,  then  it  is  impossible  to 
transfer  from  a  thing  M  to  another  thing  N,  an  influence  7, 
whether  this  influence  be  a  thing,  action,  state,  or  force. 

We  shall  demonstrate  the  validity  of  this  thesis  under 
the  three  following  cases: 

69.  CASE  I  (a).    INFLUENCE  I,  A  THING 

This  case  and  all  allied  cases  may  be  reduced  in  such  a 
manner  that  three  things  only  are  involved. 

In  Fig  11  we  show  the  factors  involved  in  Case  I  (a). 
We  assume  that  M,  N,  and  /  are  things.  At  first  hand  there 


DRY  BODY 


MOIST  BODY 


Figure  11 


SCIENTIFIC  THEISM  103 

seems  to  be  nothing  difficult  in  the  notion  that  the  thing  I 
can  separate  itself  from  M  and  pass  to  N,  causing  a  change 
in  the  latter.  Let  us  examine  the  case  more  closely.  In 
order  to  make  our  problem  definite  we  shall  suppose  that 
the  body  M  is  a  moist  body,  meaning  by  this  statement  that 
there  is  moisture  /  in  the  form  of  water  present  in  the  body 
M.  We  shall  also  suppose  that  the  body  N  is  a  dry  body, 
meaning  by  this  that  no  moisture  in  the  form  of  water  /  is 
associated  with  the  body  N.  If,  then,  we  say  that  water  7 
(being  a  real  thing  /)  passes  from  the  body  M  to  the  body 
N,  and  that  when  this  transfer  has  been  accomplished  the 
body  M,  previously  moist,  becomes  dry,  while  the  body  N, 
formerly  dry,  becomes  moist,  we  cannot  then  contend  that 
either  M  or  N  has  undergone  any  real  change.  All  that  we 
can  justly  say  is  that  the  transfer  of  7  from  M  to  N  has 
taken  place.  During  the  entire  time,  M  remained  M  and  N 
remained  N  and  neither  M  nor  N  caused  any  modification 
in  7.  On  this  assumption  our  problem  disappears,  because 
what  we  wish  to  ascertain  is  how  the  influence  7  passing 
from  M  to  N  causes  a  genuine  change  in  M  and  N.  Actual 
facts  do,  however,  bear  us  out  in  the  assumption  that  a  real 
change  has  been  produced  in  M  and  N,  for  it  is  true  that  as 
N  begins  to  get  moist,  due  to  the  incorporation  of  I,  the 
particles  of  N  are  forced  farther  apart  and  consequently 
occupy  a  greater  space  in  addition  to  a  further  change  which 
consists  in  a  modification  of  the  vigor  of  the  connection 
between  the  particles  of  N.  A  reciprocal  change  occurs  in 
M.  Upon  the  withdrawal  of  the  moisture  7,  the  drying  body 
decreases  in  volume,  its  particles  attain  closer  proximity, 
and  the  vigor  of  the  connection  between  them  undergoes  a 
change.  The  mere  recording  of  the  fact  of  transfer  of  7 
from  M  to  N  has  not  contributed  anything  to  our  knowledge 
concerning  these  real  changes  in  both  M  and  N  which  are 
simultaneous  developments.  It  is  our  desire  to  comprehend 
these  very  real  changes  in  M  and  N,  and  it  is  these  modi- 
fications which  constitute  the  gist  of  our  problem.  The 
only  result  accomplished  is  a  new  disposition  of  the  seat 
of  our  problem.  Our  query  takes  a  new  and  more  definite 
form  in  that  we  now  seek  to  comprehend  how  the  presence 
of  water  7  in  N  produces  a  change  in  N,  and,  moreover,  how 
the  withdrawal  of  7  is  a  fact  sufficiently  potent  to  account 


104  SCIENTIFIC  THEISM 

for  the  modification  in  M.  Suppose  we  add  to  our  little 
world  another  body  R.  This  simple  addition  complicates 
the  problem  beyond  measure.  Now  we  are  confronted  with 
the  problem  of  a  choice,  by  the  thing  7,  of  its  final  destina- 
tion. Will  the  thing  /  choose  for  its  resting-place  the  body 
R  in  preference  to  the  body  JV?  If  we  maintain  that  the 
choice  of  /  will  be  the  body  N,  then  such  a  statement  will 
have  no  more  significance  than  if  we  maintained  that  the 
choice  must  be  the  body  R.  Moreover,  what  is  there  in- 
volved in  our  suppositions  which  will  cause  /  to  come  to  rest 
in  either  N  or  JB?  Why  not  suppose,  with  equal  show  of 
justice,  that  the  thing  I,  after  parting  company  with  M, 
avoids  the  bodies  N  and  R  and  then  tours  the  universe,  with- 
out other  aim  or  purpose,  forever?  As  we  have  already 
noted,  if  we  did  grant  that  the  thing  7  must,  for  some  super- 
rational  reason  (whatever  that  is),  proceed  to  the  body  N 
when  liberated  from  M,  then  the  mere  incorporation  of  7 
with  N  still  leaves  the  real  problem  unsolved.  In  fact,  our 
Case  I  (a)  reduces  to  Case  I  (b)  as  depicted  in  Fig.  12, 

MOIST  BODY 
DRY  BODY 


M — CONTRACTS 

^ 

N — EXPANDS 
Figure  12 

wherein  our  inquiry  involves  an  unexplained  "rapport"  be- 
tween 7  and  N.  The  existence  of  7  in  the  interstices  or  voids 
of  N  is  not  a  sufficient  reason  for  a  change  in  N.  The 
things  7  and  N  may  be  alien  and  inimical  in  their  real 
nature. 

The  friendly  services  of  the  phantom  "rapport"  cannot 
span  this  irrational  gulf,  because  we  must  insist  upon  "rap- 
port's" credentials  and  we  must  know  somewhat  of  its 
method  and  manner  of  operation. 


SCIENTIFIC  THEISM  105 

70.  CASE  II.    INFLUENCE  I,  A  FORCE,  STATE,  OR  ACTION 

The  attempt  has  often  been  made  to  avoid  the  difficulties 
of  Case  /  by  asserting  that  the  mobile  influence  is  either 
force,  action,  or  state,  and  that  /  is  not  a  thing. 

This  assumption  causes  us  to  inquire  how  a  force,  state, 
or  action  /  can  separate  itself  from  the  body  M  and  exist 
for  even  an  infinitely  short  time  as  the  force,  state,  or  action 
of  neither  M  nor  N.  What  determines  the  direction  of  /? 
Why  should  7  show  a  preference  for  N  instead  of  any  other 
body  R  of  Fig.  13? 

The  idea  that  7  is  able  to  show  a  preference  involves  the 
idea  of  a  choosing  consciousness,  and  we  are  lifted  from 
the  plane  of  matter  to  a  plane  of  non-matter,  mind,  or  spirit. 


Figure  13 


We  must  here  empnasize  this  fact  that  our  entire  discus- 
sion, viewed  retrospectively,  at  some  point  in  the  analysis 
brings  us  face  to  face  with  an  unknown  something,  other 
than  matter,  partaking  of  the  nature  of  a  selective  con- 
sciousness. 

If  we  suppose  that  at  the  time  of  the  transition  of  7  the 
body  M  is  subjected  to  a  counteraction  from  N  which  directs 
7  toward  N,  then  we  are  brought  back  to  the  original  query, 
how  N  can  influence  M  through  an  intervening  distance, 
and  how  N  can  direct  7  in  its  motion  from  M  to  N.  It  does 
not  help  the  difficulty  if  we  reverse  the  order  of  the  bodies 
in  the  above  questions  and  cast  the  onus  of  the  phenomena 


106  SCIENTIFIC  THEISM 

upon  M  instead  of  N.  Moreover,  why  should  not  7  continue 
on  forever  in  its  voyage  through  space  without  becoming 
the  state  of  N  or  R  or  anything  else  ?  If  this  is  not  the  con- 
dition which  is  produced,  and  if  7  actually  does  travel  to  N, 
then  we  are  again  confronted  with  the  idea  of  a  selective 
power  of  an  intelligent  order,  which  we  must  ascribe  to 
either  M  or  N,  whereby  the  direction  and  length  of  the  path 
of  7  are  determined.  This  means  that  our  original  problem 
is  once  more  before  us ;  that  is,  the  problem  of  how  M  or  N 
can  affect  7  at  all. 

71.  CASE  III.    CONTACT  IN  SPACE 

We  show  this  case  in  Fig.  14,  wherein  the  assumption  is 
that  contact  is  the  indispensable  preliminary  condition  for 
mutual  action.  This  assumption,  however,  is  of  no  avail, 

because  we  must  explain  why 
and  how  spatial  contact  causes 
previously  independent  and 
alien  things,  states,  or  forces 
to  become  interested  in  each 
other,  thus  producing  the  phe- 
nomena of  change.  Motion 
produced  by  impact  in  no  way 
helps  the  matter,  for  mere 
"impact"  is  not  a  "potent 

Figure  14  ...        „  ,  . 

something,  but  only  an  inci- 
dent and  an  item  amongst  many  others  involved  in  change. 
By  the  term  contact  we  must  confine  ourselves  to  either 
the  common  boundaries  of  two  objects  constituting  a  sur- 
face without  thickness,  or  a  common  point  without  exten- 
sion. It  is  evident,  then,  that  such  parts  as  comply  with 
our  true  definition  of  contact  cannot  produce  motion  in 
accordance  with  any  precept  advanced  by  science,  for  it 
can  be  only  such  molecular  portions  of  the  body  as  are  not 
in  contact  with  the  other  body  which  can  produce  motion 
in  it.  Thus  we  are  again  placed  squarely  before  our  funda- 
mental problem  of  showing  how  distant  particles  can  pro- 
duce effects  in  other  things.  After  contact  has  been  estab- 
lished we  must  inject  genuine  action  into  the  system  by 
resorting  again  to  some  influence  7  as  the  active  agent  which 
causes  change  in  the  other  body. 


SCIENTIFIC  THEISM  107 

After  contact  has  been  established  between  M  and  N, 
without  inquiring  into  the  manner  whereby  this  is  brought 
about,  the  following  represents  some  of  the  possible  changes 
which  may  take  place : 

1.  M  may  be  absored  by  N. 

2.  N  may  be  absorbed  by  M. 

3.  M  or  N,  or  both,  may  be  disintegrated. 

4.  N  may  be  set  in  motion  in  the  same  or  some  other 
direction  than  M. 

5.  N  may  remain  immovable  and  M  may  exhibit  motion 
in  an  opposite  or  some  other  direction. 

6.  Motion  of  both  M  and  N  may  cease. 

Since  mere  contact  in  space  does  not  determine  the 
choice  between  these  or  other  possibilities,  we  face  once 
more  the  ever  present  selective  intelligent  power  which 
must  be  introduced  to  make  change  a  reality  in  the  world 
of  phenomena. 

We  have  seen  that  only  those  portions  of  a  body  which 
are  not  in  contact  with  another  body  can,  under  the  preva- 
lent assumptions  of  science,  be  efficacious  in  producing 
motion,  consequently  this  very  fact  constitutes  an  admission 
that  action  at  a  distance  is  a  reality.  Action  at  a  distance, 
however,  is  inconceivable  if  we  assume  that  things  are  inde- 
pendent and  unrelated  entities.  Moreover,  we  have  seen 
that  an  influence  7,  acting  as  a  carrier  of  possible  effects,  is 
an  impossible  notion. 

Therefore  we  are  forced  to  give  up  the  notion  of  inde- 
pendent things  and  to  assert  the  mutual  dependence  of  all 
centers  of  reality  on  an  interacting  unitary  system. 

72.     The  Monon. 

What  consistent  description  can  we  give  to  these  ulti- 
mate centers  of  reality  which  we  shall  call  mononsl 

The  ultimate  particles  or  monons  must  be  genuine  uni- 
ties. The  term  unity  cannot  be  applied  to  that  which  con- 
tains independent  and  unrelated  parts  so  constituted  that 
an  experience  in  one  part  is  not  felt  with  equal  intensity  by 
all  the  other  parts.  Such  a  conglomeration  is  not  a  unity 
but  a  multiplicity  of  independent  unrelated  particles.  A 
real  unity  or  monon  M  must  be  so  constituted  that  any 
effect  or  impression  i  upon  any  one  of  its  points  a  must 


108  SCIENTIFIC  THEISM 

simultaneously  be  felt  with  equal  intensity  (i)  throughout 
the  entirety  of  M  as  a  state  of  all  of  M.  If  the  ultimate 
monon  M  is  of  such  a  nature  that  the  state  or  impression  i 
must  be  transmitted  from  point  a  of  M  to  point  b  and  then 
to  c,  from  one  point  to  another  throughout  M,  then  this  con- 
struction upon  M  is  nothing  more  than  our  ordinary  concep- 
tion of  a  number  of  distinct  an  separate  parts  or  entities, 
for  effects  are  supposed  to  be  transmitted  just  in  this  man- 
ner from  a  separate  entity  a  to  another  entity  b  and  so  on 
through  the  series  involved.  Consequently  the  concept  of  a 
real,  genuine,  unitary  monon  M  must  not  involve  the  idea  of 
the  transmission  of  an  impression  i  from  one  point  a  to  an- 
other point  b  of  M. 

The  impression  i,  whatever  be  its  nature,  must  be  simul- 
taneously felt  throughout  M  with  equal  intensity  without 
the  aid  of  a  process  of  transmission.  If  the  impression  i 
be  in  the  nature  of  a  motion,  then  the  motion  i  imparted  to 
a  point  a  of  M  must  also  be,  simultaneously,  a  motion  of  the 
point  z  of  M  located  diametrically  opposite  to  a.  In  other 
words,  no  time  must  be  consumed  in  communicating  the 
motion  from  point  a  to  point  z  along  the  line  az  of  a  monon 
M .  Moreover,  the  intensity  of  the  effect  at  z  must  be  equal 
to  the  intensity  at  a. 

The  three  elements  introduced  into  the  concept  of  the 
monon  M  are  as  follows : 

1.  Unity. 

2.  Extension. 

3.  Equality  of  the  intensity  of  imposed  effect  through- 
out the  monon. 

Actual  data  of  experience  constitute  the  only  legitimate 
test  by  which  the  validity  of  these  three  elements  may  be 
determined.  The  data  of  experience  present  nothing  ad- 
verse to  the  notion  of  unity.  Every  notion  formulated  con- 
cerning an  ultimate  particle  pictures  it  as  an  entity  and  a 
unity,  but  the  scientific  concept  of  such  a  unity  is  not  a 
critical  and  consistent  concept ;  the  word  is  merely  thought 
without  analyzing  the  implications. 

The  element  of  extension  is  taken  for  granted  by  all 
scientific  positions.  It  is  regarded  as  the  primary  fact  of 
experience.  The  third  element  which  we  have  introduced  as 
a  necessary  and  inevitable  factor  in  the  construction  of  a 


SCIENTIFIC  THEISM  109 

real  monon  is  not  borne  out  by  the  data  of  experience  if  the 
equality  of  the  intensity  is  associated  with  the  second  ele- 
ment of  extension,  because  experience  teaches  us  that 
the  intensity  of  a  force  varies,  in  some  manner,  with  the 
distance  between  the  particles.  An  ultimate  particle  com- 
posed of  disparate  independent  parts,  we  have  seen,  is  of 
no  value  in  formulating  the  conception  of  a  real  unitary 
monon.  It  is  evident  that  the  data  of  experience  force  us 
to  give  up  either  the  second  element  relating  to  extension  or 
the  third  element  relating  to  the  equality  of  the  intensity. 
We  prefere  to  give  up  the  notion  of  extension,  for  it  only 
involves  us  in  an  inexplicable  multiplicity  of  parts,  and  does 
not  involve  a  potent  dynamic  factor  which  is  the  paramount 
element  in  the  universe.  Eliminating  the  second  element, 
we  retain  for  the  monon  the  two  mutually  consistent  ele- 
ments : 

(a)  Unity. 

(b)  Equality  of  the  intensity  of  imposed  effect  through- 
out the  monon. 

In  other  words,  for  us,  unity  and  activity  are  the  vital 
elements  of  the  monon ;  extension  in  space  is  merely  a  mode 
in  which  this  active,  dynamic,  and  unitary  reality  exhibits 
itself  in  the  phenomenal  world.  Extension,  per  se,  is  not 
an  independent  dynamic  principle  of  the  world ;  it  is  impo- 
tent in  the  production  of  phenomena;  it  is  merely  one  of 
many  modes  in  which  the  real  manifests  itself.  It  is  a 
variable  phase  of  activity.  Consequently,  we  do  not  hesi- 
tate, when  consistency  demands,  to  give  up  this  notion  of 
extension  as  an  invariable  quantum  in  connection  with  our 
center  of  reality,  the  monon. 

We  therefore  reduce  the  world  to  a  system  of  unextended 
centers  of  reality  or  activity,  the  monons,  which  affect  each 
other  at  a  distance.  Through  interaction  the  monon  ex- 
hibits extension. 

The  phenomenon  of  gravitation  comes  to  our  assistance 
in  bringing  physical  evidence  before  us  which  substantiates 
our  assertions.  Gravitational  activity  is  instantaneous.  If 
gravitation  were  a  phenomenon  which  required  time  for  the 
realization  of  its  activity,  then  the  orbits  of  the  planets 
would  not  be  closed  curves  but  spirals  along  which  the 
planets  would  progress  outward  from  the  sun.  Even  for  a 


110  SCIENTIFIC  THEISM 

velocity  one  million  times  greater  than  that  of  light,  changes 
in  the  orbits  would  have  been  observed  by  astronomers. 
Since  tendencies  to  an  outward  motion  have  not  been  ob- 
served during  historic  times,  we  argue  that  gravitation  is 
not  a  time  phenomenon,  but  an  activity  which  is  instan- 
taneous in  its  effects. 

All  that  we  have  said  concerning  the  problem  of  physical 
action  holds  equally  well  for  the  ganglionic  and  commissural 
nerve-tissue  of  the  brain.  All  the  conclusions  pertain  to 
these  forms  of  activity  centers  with  equal  validity. 

73.    The  Unity  of  Things. 

We  may  represent  the  sum  total  S  of  all  cosmic  reality  by 

S  =  /|a,  b,  c, R}  =y*{Umty},  or  S= 

In  such  a  system  a  change  a  is  not  merely  a  change  of 
one  element  A,  for  the  reason  that  to  extend  the  conse- 
quences of  this  change  in  A  to  another  reality  B,  a  medium 
of  transmission  is  required ;  but  it  is  a  change  in  S  without 
the  necessity  of  a  lapse  of  time  t  before  it  becomes  a  change 
in  S.  By  the  reality  S  we  mean  an  infinitely  greater  reality 
than  the  mere  content  of  our  thought,  for  that  content 
deals  merely  with  the  eternally  subsisting  relations  of  the 
knowable.  Reality  is  forever  something  more  than 
thought.  We  regard  R,  in  the  expression 


as  the  animating  energy  of  the  world,  the  manifesting 
dynamic  principle  of  the  cosmos,  whereas  the  manifesta- 
tions, known,  unknown,  and  possible,  are  represented  by 
S.  Our  expression  is  an  equation,  therefore  we  are  not 
divorcing  content  and  reality.  For  us  content  and  reality 
are  one,  and  S  is  merely  a  function  of  R. 

A  crude  mathematical  analogy  to  the  interaction  be- 
tween activity  centers  in  this  unitary  system  called  the 
cosmos  is  found  in  the  infinite  series 

i>  it  i>  A* -srlim  rais** • » •  •  to  infinity. 

A  successive  summation  of  terms  gives  us 

ii  f,  f»  if, 1 1W,  *Htf» approaching  1. 

The  summation  is  an  infinite  process  which  cannot  be 
accomplished  in  time.  Nevertheless,  we  know  definitely 


SCIENTIFIC  THEISM  111 

that  if  we  continue  the  summation  indefinitely  the  total 
sum  can  never  exceed  unity.  There  are  possible  an  in- 
finite number  of  terms;  nevertheless,  the  sum  of  this  in- 
conceivable totality  cannot  exceed  unity.  Suppose,  now,  that 
a  change  in  the  first  term  occurs  so  that  ^  becomes  1/3, 
then  this  may  be  compensated  by  a  change  in  the  second 
term  from  1/4,  to  5/12;  in  other  words,  the  first  term  has 
been  decreased  by  1/6  and  the  second  term  has  been  in- 
creased by  the  same  amount,  consequently  no  change  in  the 
totality  of  S  has  occurred.  Innumerable  similar  compen- 
sating changes  may  be  imagined  to  take  place  in  any  or 
all  the  terms  of  S  without  affecting  the  total  which  S 
represents. 

It  is  evident  that  this  crude  analogy  cannot  do  justice  to 
what  we  desire  to  express  by  S  being  a  function  of  R  and 
equalling  unity,  for  we  never  will  be  able  to  state  the  com- 
plete significance  and  import  of  the  idea  R  which  we  re- 
gard as  the  vital  principle  of  the  universe. 

We  find  in  music  another  analogy  for  the  unity  which 
we  assign  to  S.  An  orchestral  production  is  a  unitary 
structure  similar  to  S.  The  orchestral  composition  is  cast 
about  a  tonic  or  keynote.  Its  part  movements  clamor  for 
resolution,  its  modulations,  anticipations,  and  cadenzas 
constitute  harmonic  structures  postulating  and  necessitat- 
ing each  other,  while  the  entire  structure  is,  verily,  a 
prayer  for  the  return  of  the  tonic. 

In  the  personal  ego  we  shall  observe  our  most  perfect 
analogy  of  the  unity  which  we  ascribe  to  S.  A  conscious 
ego  E  comprehends,  in  conjunction  with  an  act  of  the  senses, 
the  existence  of  an  a  both  as  a  something  which  enjoys  an 
individual  existence  of  its  own  and  as  a  genuine  state  of  the 
ego  E.  The  continuous  ego  reveals  to  itself,  through  mem- 
ory, both  past  and  present  as  being  the  property  of  that 
particular  ego.  It  is  this  unity  which  persists  through  a 
multiplicity  of  changing  states,  exemplified  in  the  conscious 
ego,  which  serve  as  the  microscopic  prototype  of  the  unity 
which  we  associate  with  the  idea  S. 

The  idea  S  includes  within  its  unity  all  types  and  degrees 
of  self-affirmation,  from  the  conscious  self  to  the  lowest 
form  of  a  material  unit.  Within  S,  a  thing,  therefore,  is 
merely  one  of  its  elemental  activities. 


112  SCIENTIFIC  THEISM 

74.     Can  Matter  Act  Where  It  Is  Not? 

Can  a  thing  act  where  it  is  not?  This  question  has 
deeply  disturbed  the  meditation  of  the  scientists.  Those 
who  have  replied  in  the  negative  have  presented  the  ether 
hypothesis  as  the  only  solution  remaining.  Let  us  investigate 
the  implication  involved  in  the  terms  of  the  question.  The 
word  "act"  may  be  considered  as  involving  two  factors :  (1) 
a  change  in  the  thing  itself;  and  (2)  an  influence  exerted  by 
the  thing  which  produces  a  change  in  some  other  thing  or 
things.  The  word  "thing"  may  likewise  involve  two  no- 
tions: (1)  that  things  are  unrelated  and  independent;  (2) 
that  things  are  related  and  mutually  dependent.  If  we  mean 
by  "act"  merely  a  change  in  the  thing  A,  then  it  is  evident 
that  the  thing  A  acts  only  where  it  is.  Similarly,  a  second 
thing  B  acts  only  where  it  is.  If  we  mean  by  "act"  both  a 
change  in  the  thing  A  and  the  generation  of  an  influence  I, 
then  we  are  forced  to  admit  interaction  between  mutually 
dependent  things.  This  has  been  conclusively  proved  in  the 
preceding.  Consequently,  if  we  adopt  this  latter  meaning 
for  the  word  "act,"  we  are  forced  to  the  second  conclusion 
concerning  things,  i.  e.,  that  they  are  mutually  dependent 
in  an  interacting  unitary  system.  In  addition  to  the  above, 
our  question  involves  the  notion  of  space.  The  thing  A  is 
separated  from  the  thing  B  by  a  distance  D.  Space  itself 
may  be  interpreted  in  a  twofold  manner:  (1)  it  may  be 
regarded  as  a  genuine  form  of  reality  capable  of  acting  as 
a  barrier  to  action;  (2)  space  may  be  regarded  as  merely 
a  form  of  apprehension  by  means  of  which  the  relative 
intensity  of  the  interaction  is  measured. 

The  idea  that  an  influence  I  passes  from  one  thing  A  to 
another  thing  B  has  been  shown  to  be  an  impossible  notion. 
Physical  science  cannot  point  to  one  single  instance  where 
force  has  existed,  even  for  one  moment  of  time,  as  an  inde- 
pendent entity  apart  from  matter.  Out  of  the  above  stated 
possible  combinations  depending  upon  the  significance  given 
to  the  crucial  ideas  involved  in  our  question  we  may  for- 
mulate the  following  four  tentative  assumptions : 

I.  That  things  are  independent  entities.  That  space  is  a 
barrier  or  insulator  which  prevents  action  at  a  distance. 
That  the  intervening  distance  between  things  may  be  over- 
come in  two  ways: 


SCIENTIFIC  THEISM  113 

1.  By  the  transfer  through  space  of  independent  influ- 
ences from  one  thing  to  another. 

2.  By  means  of  a  continuous  ether  which  permits  the 
transfer  of  motion  from  one  point  to  another. 

II.  That  things  are  independent.    That  space  is  not  a 
barrier  to  distance  action.    In  this  case  we  dispense  with  the 
idea  that  independent  influences  are  conveyed  from  one 
thing  to  another  thing.    This  assumption  involves  the  pos- 
sibility of  action  at  a  distance  and  consequently  a  medium 
or  ether  is  not  required  for  the  transmission  of  influences. 

III.  That  things  are  mutually  interdependent  in  a  uni- 
tary interacting  system.     That  space  is  a  barrier  to  the 
transmission  of  influences.    That  the  barrier  may  be  over- 
come in  two  ways : 

1.  By  the  transfer  through  space  of  independent  influ- 
ences from  one  thing  to  another. 

2.  By  means  of  a  continuous  ether  capable  of  transfer- 
ring influences  from  one  point  to  another.     Physical 
science  ultimately  reduces  these  influences  to  resultant 
motions. 

IV.  That  things  are  mutually  interdependent  in  a  uni- 
tary interacting  system.     That  space  is  a  form  of  appre- 
hension which  serves  merely  as  a  relative  measure  of  the 
intensity  of  the  interaction.     That  space  is  not  an  inde- 
pendent reality  capable  of  serving  as  a  barrier  to  action, 
but  that  it  is  a  form  of  apprehension  by  means  of  which  the 
perceiving  subject  becomes  aware  of  the  relative  magni- 
tude of  the  interaction. 

We  shall  now  discuss  the  relative  merits  of  the  four 
assumptions : 

Assumption  I 

We  have  already  demonstrated  the  truth  of  the  theses 
pertaining  to  Physical  Action  (see  paragraph  68  and  the 
following).  We  have  shown  that  if  we  assume  the  inde- 
pendence of  separate  things,  actions,  states,  or  forces,  then 
it  is  impossible  to  transfer  from  a  thing  A  to  another  thing 
B,  an  influence  /,  whether  this  influence  be  a  thing,  action, 
state,  or  force.  This  thesis  is  true  not  because  space  is  a 
barrier  which  prevents  action  at  a  distance,  or  action  at  all, 
but  because  the  very  assumption  that  things  are  independent 


114  SCIENTIFIC  THEISM 

creates  an  insurmountable  barrier  against  such  a  transfer. 
Space  does  not  play  the  role  of  isolator  of  things  in  the  sense 
of  creating  a  barrier  against  action.  The  difficulty  lies  not 
in  the  real  significance  of  space,  but  in  the  notion  of  the 
independence  of  things.  The  insertion  of  an  ether  or  con- 
tinuum between  thing  A  and  thing  B  is  an  attempt  to  unify 
A  and  B  so  that  A  shall  be  mechanically  connected  with  B 
because  of  an  auxiliary  binding  or  connecting  echer.  By 
its  introduction  of  the  ether  science  admits  the  fact  that 
physical  action  is  inexplicable  without  the  supposition  of 
the  unification  of  the  discrete  in  an  interacting  unitary 
cosmos.  The  artificial  mechanical  concept  of  the  ether, 
however,  cannot  unify  discreteness.  In  fact,  no  mere  act 
of  thought  can  unify  an  actual  physically  discrete  multi- 
plicity. By  this  statement  we  mean  that  a  thought  product 
like  the  ether  cannot  unify  that  which  is  already  assumed  to 
be  discrete,  separate,  and  independent.  We  must  consider 
the  unity  of  things  as  a  given  fundamental  of  reality.  When 
we  admit  this — and  admit  it  we  must — then  the  ether 
becomes  superfluous  as  a  unifying  concept.  The  principal 
function  of  the  ether  is  to  bring  about  a  condition  of  unin- 
terrupted and  continuous  contact.  We  have  already  seen 
that  contact  in  space  does  not  help  us  to  unify  discreteness 
(see  paragraph  71) .  Assuming  continuous  contact  through 
and  by  means  of  an  all-pervading  ether,  we  are  as  far 
from  an  explanation  of  physical  action  as  if  we  totally 
ignored  the  concept.  Action  at  a  distance  is  readily  under- 
stood when  we  realize  that  things  are  related  and  interact- 
ing in  a  system  which  primarily  was  and  continues  to  be 
a  unity  because  of  a  creative  and  sustaining  act  of  God. 
We  conclude  that  the  first  assumption  is  untenable. 

Assumption  11 

If  we  assume  that  space  is  not  a  barrier  to  physical  action 
at  a  distance,  this  admission  in  no  way  helps  us  to  under- 
stand the  manner  in  which  physical  action  is  brought  about 
if  we  persist  in  maintaining  the  independence  of  things. 
If  things  are  independent,  then  the  physical  universe  is 
eternally  a  chaos  out  of  which  nothing  but  the  unintelligible 
can  be  derived.  In  a  condition  of  chaos  the  causal  nexus  has 
no  meaning  and  that  uniformity  which  we  describe  in  terms 


SCIENTIFIC  THEISM  115 

of  natural  laws  has  no  significance.  The  causal  nexus  and 
uniformity  are  unthinkable  except  in  a  cosmos  which  in- 
volves relatedness  and  interdependence  in  a  system  whose 
fundamental  feature  is  unity.  We  conclude  that  whatever 
construction  is  put  upon  the  notion  of  space,  this  construc- 
tion in  no  way  modifies  the  content  of  the  notion  of  inde- 
pendence. The  fundamental  premise  that  things  are  inde- 
pendent vitiates  any  and  every  assumption  concerning  the 
nature  of  space.  We  cannot  obviate  the  implications  of 
"independence"  by  assuming  that  space  is  not  a  barrier  to 
physical  action.  For  these  reasons  we  hold  that  the  second 
assumption  is  untenable. 

Assumption  III 

The  assumption  holds  that  things  are  interdependent  in 
a  unitary  system  in  which  the  barrier  to  action  interposed 
by  the  genuine  reality  space  must  be  overcome.  We  have 
already  proved  that  independent  influences  cannot  be  trans- 
ferred through  space  from  one  thing  to  another.  We  have 
shown  that  the  concept  of  the  ether  does  not  contain  the 
solution  of  this  desired  transfer.  Moreover,  we  do  not 
admit  that  space  is  a  genuine  independent  reality  which  is 
capable  of  acting  as  a  barrier  to  physical  action.  Further- 
more, the  primary  premise  that  things  are  interdependent 
in  a  unitary  interacting  system  contains  within  itself  all 
that  is  required  to  account  for  physical  action.  Space  itself 
is  not  independent  of  interaction;  it  is  not  an  alien  entity 
foreign  to  interactions,  but  it  is  a  form  of  apprehension 
which  acquires  significance  through  interaction.  We,  the 
perceiving  subjects,  described  interaction  in  spatial  and 
temporal  terms.  Since  space  is  not  independent  of  interac- 
tion, we  conclude  that  the  terms  of  the  third  assumption  are 
mutually  incompatible  and  hence  this  assumption  also  proves 
untenable. 

Assumption  IV 

The  previous  conclusions  point  to  the  fact  that  the  terms 
of  the  fourth  premise  are  not  only  mutually  compatible,  but 
that  they  constitute  the  only  premises  under  which  physical 
action  becomes  intelligible.  Thus  we  derive  from  another 
viewpoint  the  truth  of  the  fundamental  thesis  of  interaction 
in  a  unitary  system. 


116  SCIENTIFIC  THEISM 

75.     The  Transmission  of  Motion  According  to  Physics. 

A  physicist  once  maintained  that  there  are  only  two 
ways  in  which  an  influence  can  be  transmitted  from  one 
body  to  another.  In  order  to  illustrate  his  contention  he 
took  the  case  of  two  ships  A  and  B  separated  by  a  certain 
amount  of  water  W.  The  two  methods  of  transmitting  an 
effect  or  influence  would  then  be  as  follows : 

I.  The  motion  of  ship  A  can  be  transmitted  to  ship  B  by 
means  of  the  disturbance  of  the  water  W  brought  about  by 
the  initial  motion  of  ship  A.    The  water  W  set  into  motion 
by  the  movement  of  ship  A  communicates  this  motion  to  the 
ship  B. 

II.  Ship  B  can  be  set  in  motion  by  the  impact  of  a 
cannon  ball  fired  from  ship  A. 

The  intent  of  both  cases  is  to  prove  that  action  at  a  dis- 
tance is  impossible.  We  shall  use  the  illustration  to  prove 
that  both  cases  involve  action  at  a  distance. 

The  first  case  involves  contact  between  ship  A  and  water 
W  and  also  contact  between  ship  B  and  water  W.  The  sec- 
ond case  involves  contact  between  Ship  A  and  cannon  ball  C 
and  also  contact  between  ship  B  and  cannon  ball  C  brought 
about  by  the  discharge  of  the  cannon. 

In  paragraph  71  we  have  seen  that  spatial  contact  in- 
volves either  the  common  boundaries  of  two  objects,  in 
which  case  the  boundaries  envelope  a  surface  without  thick- 
ness, or  a  common  point  without  extension.  It  is  evident 
that  such  parts  of  the  contiguous  bodies  which  comply  with 
our  true  definition  of  contact  cannot  produce  motion  in  ac- 
cordance with  any  precept  advanced  by  science,  for  it  can  be 
only  such  molecular  portions  of  the  body  which  are  not  in 
contact  with  the  other  body  which  can  produce  motion  in  it. 
Place  two  sheets  of  paper  in  contact  and  nothing  in  particu- 
lar happens  from  the  mere  contact.  No  motion  is  produced 
because  of  the  mere  contact.  If  motion  is  produced,  it  is 
due  to  some  genuine  activity  agency — the  hand,  for  ex- 
ample— located  back  of  the  common  surface  of  contact. 
Consequently  the  contact  area  between  ship  A  and  water  W 
or  cannon  ball  C  and  ship  B,  or  powder  P  and  cannon  ball  C 
has  in  itself  no  potency  to  produce  motion.  The  motion, 
then,  is  due  to  those  particles  which  are  not  located  along 
the  common  contact  surface.  These  particles  may  be  either 


SCIENTIFIC  THEISM  117 

conscious  or  unconscious  activity  centers.  There  is  no  evi- 
dence to  substantiate  the  former  supposition.  All  evidence 
points  to  the  truth  of  the  latter  assumption.  If  the  particles 
are  regarded  as  independent  entities,  they  must  be  endowed 
with  the  ability  to  choose  and  direct  the  type  of  influence 
and  the  direction  of  its  motion  to  a  preferred  destination. 
This  involves  a  conscious  volitional  activity  which  facts 
deny  to  the  material  particles.  Interaction  of  interdepen- 
dent centers  in  a  unitary  system  is  the  only  rational  solution 
of  the  problem.  The  choosing  of  the  spatial  location  and 
type  of  the  action  is  not  a  conscious  volitional  act  on  the 
part  of  the  particles,  but  it  is  a  deterministic  mode  of  inter- 
action, describable  in  terms  of  the  uniformities  called  nat- 
ural laws,  and  exhibited  in  a  unitary  system  which  reflects 
a  phase  of  the  creative  thought  of  God.  The  deterministic 
character  of  things  which  insures  uniformity  in  interaction 
is  due  to  the  imprint  of  God's  creative  thought.  This  con- 
stitutes another  proof  of  the  existence  of  God.  Returning 
to  the  consideration  of  the  component  particles  of  a  body, 
we  are  reminded  that  science  holds  that  bodies  are  composed 
of  molecules,  and  molecules  are  composed  of  atoms.  The 
atoms,  in  their  turn,  are  composed  of  sub-atomic  particles. 
None  of  these  constituent  elementals  are  regarded  by  science 
as  being  in  contact  with  each  other.  On  the  contrary,  there 
is  ample  distance  between  them  all  to  allow  for  free  orbital 
motions.  Therefore,  if  motion  results,  it  must  be  due  to 
transmitted  motion  from  particle  to  particle.  But  these 
elemental  constituents  of  bodies  never  come  into  actual  con- 
tact with  each  other  or  with  the  ultimate  constituents  of 
other  material  groups.  Therefore  action  at  a  distance  must 
take  place  between  the  elementals  of  bodies.  Consequently 
what  has  actually  been  shown  by  the  physicist,  by  the  cases 
cited,  is  that  certain  conditions  must  be  satisfied  if  this  or 
any  other  particular  phenomenon  shall  ensue.  In  the  two 
cases  mentioned  the  primary  condition  is  that  the  distances 
between  the  elementals  shall  be  small.  According  to  science, 
real  distances  intervene  between  the  elementals.  Conse- 
quently effects,  of  whatever  nature  they  may  be,  are  realized 
at  a  distance.  Therefore,  to  produce  the  phenomenon  cited, 
we  must  comply  with  those  governing  relations  which  are 
the  very  foundation  of  the  physical  universe.  In  other 


118  SCIENTIFIC  THEISM 

words,  for  the  cases  quoted,  we  cannot  expect  motion  to 
result  in  ship  B  if  ship  A  is  placed  in  an  empty  portion  of 
space  far  removed  from  ship  B.  The  fact  that  this  hypo^ 
thetically  empty  space  is  devoid  of  matter  is  not  the  reason 
for  the  failure  to  produce  the  phenomenon ;  for  whether  the 
void  be  small,  as  in  the  case  of  the  voids  between  the  ele- 
mentals  of  bodies,  or  great,  as  assumed  in  the  hypothetical 
case  in  which  ship  A  is  placed  in  a  vacuum  far  remote  from 
ship  B — in  either  case  we  deal  with  a  void  equally  uncon- 
querable for  the  physicist  who  obstinately  refuses  to  grant 
the  possibility  of  that  which  always  is  involved  in  physical 
action;  that  is,  action  at  a  distance.  We  draw  the  further 
self-evident  conclusion  that  intervening  distance  is  merely 
a  measure  of  the  nearness  or  remoteness  at  which  a  particu- 
lar phenomenon  may  result.  For  instance,  if  we  wish  cer- 
tain types  of  chemical  action  to  take  place,  we  must  arrange 
conditions  so  that  the  intervening  distances  are  exception- 
ally small  in  addition  to  providing  for  the  free  mobility  of 
the  particles.  This  we  accomplish  by  solutions  and  the 
electric  furnace.  Space,  then,  is  a  chart  of  the  relative  inter- 
action intensity  values.  Space  is  meaningless  as  an  inde- 
pendent reality. 

At  this  point  in  the  argument  the  physicist  produces  his 
jug  of  ether,  saying,  "Let  me  pour  this  stuff  freely  into  the 
universe  and  all  your  troubles  are  solved.  My  ether  is  the 
most  pliable  concoction  imaginable.  It  is  rarer  than  the 
rarest  gas,  but  whenever  occasion  demands  it  becomes  so 
rigid  that  it  can  withstand  a  pressure  of  37,000  tons  per 
square  inch  (according  to  Maxwell).  In  comparison  with 
the  rigidity  of  high-carbon  steel,  whose  ultimate  strength  is 
about  fifty  tons  per  square  inch,  my  ether  is  a  giant.  Fortu- 
nately for  the  planets  and  atoms,  my  giant,  although  over 
seven  hundred  times  more  rigid  than  high-carbon  steel,  is 
very  sympathetic,  and  allows  them  to  pass  right  through 
him  without  causing  either  him  or  them  the  slightest  incon- 
venience or  pain." 

The  purpose  of  the  ether,  then,  is  to  do  for  a  particle  A 
and  another  particle  B  what  the  water  W  was  supposed  to 
do  for  the  ship  A  and  the  ship  B.  The  problem  is  identically 
the  same  in  either  case.  In  both  cases  it  is  an  attempt  to 
account  for  physical  action  through  spatial  contact.  That 


SCIENTIFIC  THEISM  119 

this  attempt  fails  utterly  has  already  been  shown.  Mere 
contact  between  particle  A  and  ether  E  can  never  explain 
the  transfer  of  an  influence  /  from  particle  A  to  ether  E. 
It  is  really  an  attempt  to  establish  interaction  and  to  create 
a  unity  out  of  the  discrete  particles  of  the  universe.  No 
artificial  thought  product  like  the  ether  can  ever  unify 
the  physically  discrete.  If  the  unity  does  not  actually  exist, 
then  a  mere  thought  concoction  can  never  produce  a  genu- 
ine physical  unity.  We  maintain  that  the  unity  of  things  is 
a  real  given  exemplified  in  interaction.  Therefore  we  need 
no  artificial  ether  concept  to  unify  the  physical  universe. 

Finally,  the  physicist  will  maintain  that  all  is  ether  and 
that  the  discrete  particles  are  merely  manifestations  in  the 
ether  and  of  the  ether.  This  is  his  final  and  most  consistent 
attempt  to  produce  unification.  Unfortunately,  he  must 
localize  the  disturbances  in  the  ether  in  order  to  give  a 
semblance  of  physical  reality  to  his  ether  particles.  In 
other  words,  he  introduces  discreteness  into  his  continuum 
and  thus  breaks  down  his  own  parent  concept.  If  there 
be  no  discreteness,  then  the  empty  void  is  as  potent  a  notion 
as  the  continuum  or  ether.  The  moment,  however,  that  the 
physicist  localizes  the  ether  particle,  differentiates  it,  as  it 
were,  into  discrete  nodes,  vortices,  centers,  waves,  or  what 
not,  then  he  is  face  to  face  with  all  the  difficulties  already 
considered  under  the  caption  of  "The  Problem  of  Physical 
Action"  (see  paragraph  68  and  the  following).  He  must 
show  how  an  influence  /  can  be  properly  transferred  in  the 
right  direction  and  through  the  correct  distance  from  an 
ether  center  A  to  another  ether  center  B.  If  the  ether  cen- 
ters be  regarded  as  independent,  then  this  ether  concept  will 
involve  the  same  insurmountable  difficulties  as  are  met  with 
in  the  case  of  empty  space.  If  he  admits  our  primary  con- 
tention that  the  ultimate  centers,  whatever  be  their  nature, 
are  interdependent  and  interacting  in  a  unitary  system, 
whatever  be  the  nature  of  that  system,  then  his  ether  be- 
comes superfluous  even  if  it  could  be  made  to  be  self-con- 
sistent. We  have  shown  that  the  ether  is  far  from  self- 
consistent.  We  have  shown  that  physical  action  is  impossible 
except  under  the  assumption  that  the  physical  universe 
is  a  cosmos  of  related  interacting  things.  For  the  above- 
stated  reasons  we  hold  that  the  ether  is  inconsistent  and 


120  SCIENTIFIC  THEISM 

superfluous.  Consequently  we  maintain  that  the  physicist 
has  failed  in  his  attempt  to  unify  the  physical  universe 
by  the  concept  of  the  ether.  It  follows  that  he  has  no 
alternative  left  but  the  acceptance  of  the  truth  of  action  at 
a  distance. 


CHAPTER  V 

THE  MODEL  OF  THE  PHYSICAL  UNIVERSE  ACCORDING  TO 
THE  SPACE-TIME  POTENTIAL 

76.    The  Real  Purpose  of  the  Ether. 

There  are  almost  as  many  ethers  as  there  are  physicists. 
Certain  resemblances  to  matter  are  evident  in  every  ether 
hypothesis.  The  ether  model  is,  in  fact,  always  based  upon 
certain  fundamental  properties  of  matter,  reduced  either  to 
zero  or  raised  to  the  nth  power.  The  continuous  occupation 
of  space  seems  to  be  common  to  all  of  them.  Matter  is  here 
and  there.  Ether  is  supposed  to  be  everywhere;  hence  we 
have,  in  the  notion,  the  space  occupation  of  matter  raised  to 
the  nth  power.  The  ether  is  a  kind  of  maximum  and  mini- 
mum of  matter  properties.  The  theory  was  first  announced 
by  Huyghens  and  later  it  was  developed  by  Young  and 
Fresnel.  At  the  outset  it  was  a  protest  against  the  emission 
theory  of  Newton.  If  it  is  thought  of  as  a  solid,  it  is  en- 
dowed with  incompressibility.  Other  thinkers  ascribe  in- 
finite compressibility  to  the  ether;  in  either  case,  matter 
properties  extended  to  an  ultimate  limit.  F.  Neumann  and 
MacCullagh  adhered  to  the  incompressibility  notion,  while 
Fresnel  preferred  the  hypothesis  of  infinite  compressi- 
bility. Hertz  refers  to  it  as  an  isotropic,  homogeneous  and 
restraining  medium.  Lord  Kelvin  originated  the  gyrostatic 
ether  model.  We  are  told  by  some  that  the  ether  is  struc- 
tureless, incompressible,  motionless,  but  capable  of  being 
set  in  motion,  non-elastic,  capable  of  indefinite  subdivision, 
and  that  the  resulting  parts  can  move  over  each  other  with- 
out friction.  No  known  reality  in  the  universe  satisfies 
these  specifications.  Empty  space  (vacuum)  qualifies  bet- 
ter than  any  form  of  matter.  After  all  is  said,  the  ether  is 
merely  an  imagined  realization  of  the  desire  that  at  every 
instant  there  shall  everywhere  be  something  which  is  in 
intimate  responsive  connection  with  matter.  Sometimes  the 

121 


122  SCIENTIFIC  THEISM 

ether  is  regarded,  after  the  analogy  of  a  fluid,  as  an  infi- 
nitely compressible  homogeneous  fluid.  Then  again,  the 
solid  to  the  ?ith  power  becomes  the  model.  As  a  solid  it  is 
considered  by  some  as  movable  and  by  others  as  immovable. 
Matter  becomes  the  place  of  a  single  particle  of  this  etherial 
substance.  By  some  the  material  ether  particle  is  regarded 
as  a  hole  in  the  ether,  and  by  others  as  a  vortex  or 
a  point  of  torsion.  The  elements  of  the  ether  concept, 
finding  their  original  source  in  the  properties  of  matter, 
are  carried  so  far  beyond  the  nature  of  this  source  that 
they  become  inoperative.  It  is  further  demanded  of 
this  ether  substance  that  it  shall  serve  as  a  medium  for  the 
propagation  of  all  that  varied  class  of  vibratory  motion 
which  apparently  fails  to  find  an  adequate  explanation 
under  the  old  emission  theory.  Then  again  it  seems  desir- 
able that  the  ether  shall  be  capable  of  exerting  pressure 
upon  such  moving  elementaries  as  electrons.  This  is  par- 
ticularly true  in  the  theory  of  Lorentz.  The  difficulties 
encountered  in  reconciling  these  demands  placed  upon  the 
ether  model,  constructed  from  the  physical  properties  of 
matter  expanded  or  contracted  so  far  beyond  the  bounds 
of  reality  that  they  become  either  inconceivable  or  self- 
contradictory,  are  so  insurmountable  that  many  serious 
investigators  have  concluded  that  the  notion  is  totally  inade- 
quate properly  to  correlate  the  ever-growing  array  of 
experimental  facts. 

The  apartness  and  independence  of  matter  is  the  basic 
fact  underlying  the  desire  "that  at  every  instant  there  shall 
everywhere  be  something  which  is  in  intimate  responsive 
connection  with  matter."  Is  there  that  which  can  accom- 
plish this  without  including  the  objectionable  elements  in 
the  ether  model?  Many  facts  point  toward  fruitful  chan- 
nels along  which  consistent  development  may  proceed.  If 
we  abandon  the  idea  that  material  centers  are  self-sufficient 
and  independent  except  under  localized  conditions,  then  we 
have  removed  the  greatest  difficulty  in  the  way  of  under- 
standing any  and  every  type  of  phenomenal  activity.  In 
other  words,  admit  interaction  in  a  unitary  system  of  inter- 
related centers,  and  the  terrors  of  the  vacuum  disappear. 
It  was  this  very  dread  of  a  vacuum  which  called  forth  the 
desire  that  "there  shall  everywhere  be  something." 


SCIENTIFIC  THEISM  123 

77.    The  Concurrent  System. 

In  the  further  development  of  our  model  to  meet  the 
requirements  of  class  phenomena,  we  must  adhere  com- 
pletely to  those  basic  distinctions  and  properties  which  con- 
stitute our  concept  of  matter.  We  must  neither  minimize 
nor  maximize  these  properties.  Were  we  to  find  that  matter 
is  materialized  energy — that  is,  an  ultimate  particle  is  a 
work  center — this  discovery  (already  a  fact)  must  not  and 
cannot  affect  the  nature  of  that  primitive  content  of  matter 
which  we  shall  employ  in  our  model.  The  concurrent  sys- 
tem or  vehicle  we  desire  can  be  ultra-material  only  in  the 
sense  that  it  may  be  constructed  from  the  very  ultimates  of 
matter.  It  must  not  be  ultra-material  in  the  sense  that  we 
can  carry  the  properties  of  matter  to  their  zero  or  infinite 
limits.  Our  concurrent  system,  composed  of  the  ultimates 
of  matter,  may  be  thought  of  as  emanating  from  or  con- 
centrated within  matter  in  accordance  with  the  require- 
ments of  the  particular  activity. 

The  motions  of  these  ultimates  must  be  connected  with 
the  motions  of  their  related  matter  groups.  Through  the 
varied  relations  between  bodies  we  may  know  these  vehicle 
ultimates,  if  not  in  their  direct  effects,  then  through  their 
indirect  effects.  The  further  extension  of  the  concurrent 
system  along  surfaces  in  space  may  be  contemplated  as  con- 
sisting in  the  interaction  of  the  ultimate  centers  disposed 
in  configurations  which  insure  equilibrium.  Such  spatial 
surfaces  would  constitute  resistive  fields  of  centers  inter- 
acting at  a  distance,  for  matter  is  discrete  and  not  continu- 
ous. Motion  cannot  be  comprehended  upon  any  other  basis 
than  that  of  actual  observed  motion,  which  always  presup- 
poses discrete  particles  capable  of  genuine  displacement  for 
the  very  reason  that  they  are  discrete.  Action  at  a  distance, 
regarded  as  interaction  between  related  centers  in  a  unitary 
system,  far  from  being  inconceivable,  is  the  only  assumption 
which  is  consistent  and  in  accord  with  reality.  In  the  gravi- 
tational activities  we  have  a  universal  exemplification  of 
action  at  a  distance.  All  attempts  which  have  been 
made  to  escape  this  conclusion  concerning  gravitational 
action  have  had  recourse  to  the  ether  hypothesis,  which, 
as  we  have  seen,  contains  the  seeds  of  its  own  destruc- 
tion. 


124  SCIENTIFIC  THEISM 

78.    Fields  of  Interaction. 

The  resistive  fields  are  really  fields  of  interaction  which 
may  be  regarded  as  both  resistive  and  receptive.  Space  may 
be  considered  as  laminated  in  every  direction  with  such 
fields.  Empty  space  has  no  meaning  from  this  point  of 
view,  for  the  reason  that  every  surface  in  space  is  subjected 
to  interaction,  which  results  in  giving  to  every  one  of  its 
points  a  definite  work  or  energy  value.  The  motion  of  a 
particle  within  a  given  surface  can  be  definitely  predicted 
if  we  have  a  prevision  of  the  work  value  of  the  points  in 
the  surface.  Our  model,  therefore,  may  include,  without 
inconsistency,  planes  and  surfaces  free  from  ultimate  cen- 
ters because  such  planes  will  still  have  definite  energy  sig- 
nificance for  every  point  within  them.  If  a  particle  A  moves 
into  an  interacting  field  containing  n  ultimates,  then  the 
future  motion  depends  upon:  (1)  its  actual  position  in  the 
field;  (2)  its  mass;  (3)  its  velocity;  (4)  the  force  condition 
of  the  field  due  to  the  precise  interaction  at  the  moment  con- 
sidered. Moreover,  the  force  conditions  of  the  field  depend 
upon :  (1)  the  precise  location  of  the  n  ultimates  within  the 
field  and  their  complete  interaction,  which  must  include 
themselves  and  all  the  other  ultimates;  and  (2)  the 
previous  motion  and  interaction  condition  of  the  par- 
ticle A. 

79.     The  Scientific  Renaissance. 

When  the  true  nature  of  the  electron  was  established, 
science  was  born  again.  Matter  was  then  forever  dethroned 
and  the  energy  phase  was  restored  to  its  rightful  heritage  in 
the  realm  of  knowledge.  Seers  like  Ostwald  realized  the 
truth  that  energy  is  the  inclusive  action  phase,  while  matter, 
as  a  separate  independent  entity,  is  the  phantom  of  the 
imagination.  It  remained  for  J.  J.  Thomson  to  demon- 
strate this  experimentally.  As  one  manifestation  of  energy 
matter  is  truly  real,  but  as  something  alien  to  energy,  a 
dark  unrelated  background  for  the  drama  of  physical  action, 
as  such  matter  has  no  reality.  Matter  is  of  energy,  not 
independent  of  energy,  and  energy  itself  is  merely  a  phase 
of  interaction. 

This  epoch-making  discovery  began  with  Varley's  ob- 
servations of  the  cathode  rays  wihch  are  given  off  at  the 


SCIENTIFIC  THEISM  125 

cathode  in  a  vacuum  tube  filled  with  a  very  dilute  gas  when 
electricity  is  passed  through  the  tube.  These  cathode  rays 
travel  with  great  velocity  from  cathode  to  anode,  and  they 
carry  a  negative  electrical  charge.  They  are  deflected  in 
the  same  direction  in  a  magnetic  field  as  negatively  charged 
particles.  Thomson  showed  that  cathode  rays  behave  like 
negatively  charged  particles  in  an  electrical  field.  Thomson 
called  them  "corpuscles."  Johnstone  Stoney  named  them 
"electrons."  It  has  also  been  shown  that  the  beta  rays  given 
off  by  radium  are,  in  fact,  nothing  but  electrons.  The  mass 
of  the  sub-atomic  electrons  remains  practically  constant  at 
about  (1-4-1845)  of  the  mass  of  the  hydrogen  atom,  pro- 
vided that  the  velocity  remains  within  certain  definite  lim- 
its. Beyond  the  extreme  limit  the  variation  in  the  mass  of 
the  electron  is  marked,  and  experimental  evidence  has  shown 
that  the  mass  then  increases  with  an  increase  in  the  velocity 
of  the  electron. 

To  Kaufmann  belongs  the  credit  for  this  astounding  dis- 
covery, which,  in  the  hands  of  Thomson,  gave  us  a  new 
conception  of  matter.  The  startling  fact  is  that  the  actual 
mass  increase  is  exactly  what  it  must  be  if  the  mass  is 
entirely  electromagnetic.  The  electronic  particles  are  devi- 
ated by  magnetic  or  electrical  forces.  The  amount  of  this 
deviation,  the  charge  transferred,  and  the  heat  developed 
constitute  some  of  the  basic  data  from  which  the  mass  of 
the  electron  is  determined.  In  the  Newtonian  dynamics  we 
have  seen  that  force  is  the  product  of  mass  and  acceleration 
under  the  supposition  that  the  mass  remains  constant.  For 
the  electron  the  Newtonian  law  apparently  holds  good  while 
the  mass  remains  constant.  The  old  expression  must  be  so 
modified  that  it  will  provide  for  this  variation  in  the  mass. 
The  old  Newtonian  expression  involves  one  constant  and 
one  variable;  the  modified  Newtonian  expression  must  in- 
clude two  variables.  These  radical  discoveries  have  com- 
pletely effaced  the  dogma  of  a  fixed  and  solid  atom.  The 
invariability  of  mass  is  gone  forever. 

80.     The  Normal  Materialization  of  the  Concurrent  System. 

Can  the  concurrent  system  be  transformed  into  normal 

matter?    In  order  to  answer  this  question  let  us  consider 

a  simple  device  composed  of  a  horseshoe  magnet  whose  two 


126  SCIENTIFIC  THEISM 

branches  culminate  in  a  single  cylindrical  shaft  very  much 
like  the  shape  of  an  ordinary  tuning-fork.  The  cylindrical 
shaft  is  provided  with  a  bearing  in  a  vertical  conducting 
support  which  is  properly  insulated  from  the  base  of  the 
apparatus.  A  crank  is  attached  to  the  end  of  the  cylindrical 
shaft.  Parallel  to  the  ends  of  the  horseshoe  magnet  we  erect 
an  iron  plate  in  a  vertical  position,  taking  care  to  insulate 
this  also  from  the  common  base  of  the  device.  A  copper  wire 
is  connected  with  the  iron  plate.  Another  copper  wire  is  con- 
nected with  the  conducting  vertical  support.  Ordinarily 
we  say  that  the  iron  plate  opposite  the  magnet  is  mag- 
netized. Moreover,  this  induction  reacts  upon  the  magnet, 
apparently  strengthening  its  magnetism.  The  positive  and 
negative  poles  of  the  magnet  produce  respectively  negative 
and  positive  poles  in  the  plate.  We  assume  that  the  space 
between  the  generated  magnetic  poles  in  the  iron  plates  and 
the  poles  of  the  magnet  contains  the  primary  matter  of  the 
concurrent  system.  By  the  term  "matter"  we  mean  an 
action  center  or  group  of  centers.  An  action  center  is  a 
mass-acceleration  center  according  to  the  force-center  the- 
ory of  Boscovich.  Primary  matter  is  capable  of  phase 
transformation.  (This  will  be  discussed  in  detail  later.) 
By  the  expenditure  of  work  primary  matter  can  be  trans- 
formed into  secondary  or  normal  matter.  The  electron  is 
the  unit  of  normal  matter.  The  atom  and  molecule  are 
aggregates  of  these  normal  matter  units. 

Let  us  now  connect  the  two  copper  wires,  establishing 
a  complete  circuit  through  some  device  which  will  tell  if  a 
current  of  electricity  is  produced.  Nothing  happens.  Now 
let  us  turn  the  crank  of  the  magnet  vigorously.  The  instant 
that  we  do  this,  something  happens ;  in  fact,  we  produce  an 
electric  current  which  can  be  made  to  do  many  kinds  of 
work.  We  observe  further  that  effort  is  required  to  turn 
the  crank  just  as  if  a  resistive  pressure  were  being  applied 
to  the  shaft.  When  we  cease  turning  the  crank  the  electric 
current  ceases.  The  magnet  and  the  iron  plate  show  no 
loss  of  material  whatever,  indicating  that  the  current  is  not 
produced  by  modifications  of  that  type.  In  fact,  the  electric 
current  generated  is  due  to  the  expenditure  of  energy  in- 
volved in  the  turning  of  the  crank  against  a  resistance. 
Now  the  new  school  of  science  tells  us  that  an  electric  cur- 


SCIENTIFIC  THEISM  127 

rent  is  merely  a  flow  of  electrons.  It  is  incontrovertible  that 
the  expenditure  of  nothing  but  energy,  in  our  device,  has 
generated  an  electric  current,  which  means  a  flow  of  elec- 
trons. Two  questions  will  occur  to  us :  (1)  Did  we  actually 
make  these  electrons  and  also  set  them  in  action  by  expendi- 
ture of  energy  ?  (2)  Did  we  merely  set  them  in  motion  ?  Ac- 
cording to  the  new  school,  all  matter  is  made  from  electrons, 
and  an  atom  is  a  miniature  solar  system  wherein  the  elec- 
trons are  the  planets.  Perhaps  the  electrons  which  consti- 
tute the  current  of  electricity  are  detached  from  the  magnet 
and  the  iron  plate,  and  the  energy  expended,  in  our  device,  is 
required  to  separate  them  from  the  iron  atoms  and  to  keep 
them  in  motion.  If  continuous  work  is  to  be  done  in  the 
external  circuit,  a  continuous  flow  of  electrons  must  be 
maintained.  This  means  the  ultimate  complete  disintegra- 
tion and  dissipation  of  the  iron  atoms,  which  is  not  borne 
out  by  fact.  Unless  there  is  some  other  source  of  supply 
of  electrons,  it  would  seem  that  our  device  actually  converts 
energy  into  electrons.  From  the  new  viewpoint  this  is  not 
alarming  because  it  is  conceded  that  the  entire  mass  of  the 
electron  is  of  electrical  origin.  We  can,  then,  take  the 
position  that  every  point  in  space  exhibits,  or  is  capable  of 
exhibiting,  a  definite  work  or  energy  value,  thus  constitut- 
ing an  interacting  etherless  system,  able,  under  determinate 
conditions,  to  produce  that  change  and  transformation  of 
energy  which  we  call  matter.  Nothing  of  real  import  can 
be  maintained  against  this  view ;  in  fact,  it  must  remain  as 
the  basic  groundwork  of  any  hypothesis  which  is  to  do  jus- 
tice to  physical  action.  However,  the  value  of  a  physical 
model  must  not  be  underestimated  because  of  the  possibility 
which  it  provides  for  previsions  and  subsequent  progressive 
corrections. 

The  model  of  the  concurrent  system  composed  of  primary 
matter  must  therefore  be  conceived  as  having  already  pres- 
ent within  it  partially  developed  energy  manifestations 
located  at  positions  compatible  with  ascertainable  physical 
requirements.  Interaction  between  the  intrinsic  energy  of 
the  concurrent  system  and  the  extrinsic  energy  associated 
with  already  developed  matter  groups  may,  then,  produce 
amplification  and  more  complete  development  of  the  energy 
factors  of  the  concurrent  system. 


128  SCIENTIFIC  THEISM 

81.     The  Monon. 

Indications  point  strongly  to  the  conclusion  that  all  phe- 
nomenal manifestations  of  energy  ultimately  prove  to  be  of 
the  kinetic  order.  From  this  standpoint  our  spatial  back- 
ground is  a  chart  of  potential  energy  values  in  which  kinetic 
energy  of  definite  magnitude  is  manifest  at  definite  positions 
or  points.  At  such  positions,  then,  we  must  locate  our  activ- 
ity of  kinetic  energy  centers,  which,  for  want  of  a  definite 
name,  we  may  call  monons.  We  must  ascribe  to  these 
monons  such  basic  properties  as  form  the  fundamental 
requirements  of  possible  matter.  The  monons,  in  addition 
to  being  energy,  are  potential  normal  matter.  Therefore  we 
assign  to  them  the  fundamental  property  or  capacity  of 
exhibiting  resistance  to  that  which  tends  to  give  them  accel- 
eration; in  other  words,  we  attribute  kinetic  reaction  to 
them  as  their  basic  phenomenal  property.  Since  the  concept 
of  kinetic  reaction  includes  the  idea  of  resistance,  we  have  at 
once  the  negative  feature  of  our  monon ;  and  since  they  are 
capable,  through  their  own  positive  content  of  kinetic 
energy,  of  exhibiting  interaction,  we  also  attribute  a  positive 
nature  to  this  ultimate  element.  Interaction  requires  the 
unified  presence  of  both  the  negative  and  the  positive  nature 
in  the  monon,  the  former  to  insure  its  self-preservation  and 
survival,  the  latter  to  provide  for  possible  attractive  mani- 
festations. This  is,  in  fact,  what  interaction  means,  repul- 
sion and  attraction,  reaction  and  action,  unified  in  the  con- 
tent of  the  monon.  We  cannot  conceive  of  the  independent 
existence  of  either  the  negative  or  the  positive  function 
within  the  primary  unity.  Complexities  built  up  of  monons 
must  behave  in  this  twofold  manner.  Complexity  does  not 
prohibit  unity :  it  is  unity  of  a  higher  order  ascending  until 
consciousness  is  attained.  The  universe  itself  is  the  highest 
physical  type  of  unity  in  complexity. 

Since  kinetic  reaction  involves  a  possible  mass  coupled 
inseparably  with  a  possible  acceleration,  we  include  these 
factors  in  the  concept  of  the  monon  with  full  realization  that 
mass  and  acceleration  are  naturally  dependent  variables 
capable  of  all  the  shades  of  variability  from  zero  to  a  pos- 
sible maximum.  Within  certain  critical  values  we  may  there- 
fore find  that  the  variation  of  the  mass  is  practically  re- 
duced to  its  zero  limits ;  in  other  words,  below  this  critical 


SCIENTIFIC  THEISM  129 

value  the  mass  may  appear  to  be  maintained  at  a  constant 
value.  We  do  not,  therefore,  regard  the  monon  as  an  abso- 
lutely fixed  and  unchanging  ultimate.  Moreover,  as  a  cen- 
ter of  static  influence  its  scope  of  activity  must  include  a 
maximum  and  minimum  sphere  within  which  limits  expan- 
sion and  contraction  are  possible.  We  look  upon  the  monon 
as  being  capable  of  this  form  of  pulsation  between  definite 
limits.  The  monon,  then,  is  energy  manifest  within  definite 
limits  responsive  to  the  general  law  of  interaction. 

82.     The  Energosial  or  Concurrent  System. 

The  further  development  of  our  model  requires  that  its 
kinetic  energy  be  defined,  in  part,  in  terms  of  motion,  for 
the  reason  that  all  physical  phenomena  are  ultimately  re- 
duced to  terms  of  motion.  This  involves  the  existence  of 
gyrational  groups  of  monons.  If  our  concurrent  system,  or 
energos  (meaning  "active"  or  "in  work"),  is  energy,  it 
does  not  become  necessary  to  think  of  the  manner  of  the 
beginning  of  these  gyrations,  because  they  are  merely  one 
means  of  exhibiting  this  eternal  energy.  The  maintenance 
of  the  gyration  is  no  more  the  problem  of  science  than  the 
seeking  for  a  cause  or  manner  of  the  beginning.  The  con- 
tinuously given  world  involves  the  continuous  presence  of 
energy.  The  continuous  maintenance  of  energy  forces  us  to 
admit  the  immanence  and  transcendence  of  that  activity 
principle  known  to  philosophy  as  the  Absolute  and  to  the 
religious  consciousness  as  God.  If  our  model  becomes  a 
better  interpreter  of  physical  action  by  adding  to  it  the 
idea  of  gyrational  groups,  then  we  must  consider  them  also 
as  continuously  given  because  they  are  our  mechanical  sym- 
bol of  an  ever-present  energy.  This  does  not  preclude  vari- 
ations in  the  velocity  and  size  of  the  gyrational  orbit;  in 
fact,  this  must  be  assumed  if  our  model  shall,  even  with 
partial  success,  portray  physical  action.  Moreover,  we  must 
include  the  possibility  of  dismemberment  of  the  groups, 
involving  curvilinear  and  rectilinear  motions  of  the  dismem- 
bered centers.  We  do  not  desire,  therefore,  like  Helmholtz 
and  Kelvin,  to  maintain  the  eternal  gyration  of  our  groups. 
The  condition  of  a  group  is  not  only  due  to  self-determina- 
tion, but  it  is  also  dependent  upon  other  interaction  factors. 
The  maintenance  of  the  world  is  provided  for  in  the  con- 


130  SCIENTIFIC  THEISM 

tinuous  manifestations  of  our  concurrent  system,  the 
energos  together  with  the  conservation  of  those  matter 
groups  which  we  may  regard  as  external  to  this  system. 
This  continuous  manifestation  is  grounded  in  the  concept 
of  God. 

83.     The  Gyratory  Energons. 

Gyratory  Groups 

A  rotary  system  composed  of  diametrically  oppo- 
site monons  constitutes  our  simplest  gyratory  group.  In 
order  to  refer  to  this  group  type  we  shall  call  them  energons. 
This  name  will  suggest  their  origin  in  the  "energosial"  sys- 
tem. Far  from  the  influence  of  disturbing  matter  groups, 
the  diameter  of  the  energons  will  be  practically  equal  to 
each  other  and  constant.  If  a  body  is  free  to  move  in  a 
plane  wherein  the  components  of  the  activity  intensities  due 
to  the  external  system,  resolved  along  suitable  reference 
axes,  are  equal  to  each  other,  then  it  will  move  in  a  circular 
orbit.  If  these  component  intensities  are  unequal,  the 
orbit  will  be  a  conic  section.  The  monons  constituting 
the  energon  are  therefore  free  to  move  in  the  same  circular 
orbit  if  the  component  activity  intensities  of  the  system 
external  to  themselves  are  equal  to  each  other.  In  other 
words,  the  nature  of  the  orbit  may  be  considered  to  be  gov- 
erned by  the  external  activity  factors.  We  may  look  upon 
the  result  as  a  centripetal  effect  tending  to  maintain  the 
monons  in  a  constant  radial  relation  to  a  common  center.  If 
we  neglect  the  part  played  by  the  monons,  our  concept  will 
be  incomplete.  The  energon  and  the  external  system  interact 
continuously.  In  this  case,  then,  the  role  assigned  to  the  mo- 
nons would  be  one  of  mutual  repulsion,  which,  in  reference 
to  the  external  system,  would  constitute  a  centrifugal  reac- 
tion. A  central  force  would  produce  the  same  result  both 
in  respect  to  the  type  of  the  orbit  and  the  action  intensities, 
provided  that  the  effect  of  the  system  external  to  the  energon 
be  totally  disregarded.  We  cannot  disregard  the  entire  uni- 
verse for  the  sake  of  merely  establishing  the  rotation  of 
one  of  its  groups,  consequently  we  are  forced  to  look  upon 
the  gyration  as  being  due  to  the  interaction  of  both  the  ex- 
ternal system  and  the  energon  as  heretofore  set  forth.  The 


SCIENTIFIC  THEISM  131 

external  system  would  therefore  exhibit  an  intensity  of 
action  equivalent  to  the  kinetic  reaction  developed  by  the 
rotating  energon.  From  another  viewpoint,  the  reaction 
of  the  concurrent  system  is  equivalent  to  the  centrifugal 
force  of  the  energon.  The  concurrent  system  and  the  gyrat- 
ing energon,  therefore,  exist  in  a  condition  of  "dynamic  equi- 
librium." An  influx  of  energy,  due  to  the  action  of  a  mate- 
rial group,  into  the  energonic  system  would  be  in  the  nature 
of  an  increase  in  the  centrifugal  force  causing  an  increase 
in  the  radius  of  the  energon. 

84.     The  Birth  of  the  Electron. 

Let  us  again  refer  to  our  current  generator.  First  we 
must  consider  the  role  played  by  the  constituent  members  of 
the  device.  From  our  present  viewpoint  we  regard  a  mag- 
netic substance  as  capable  of  exhibiting  exceptional  perme- 
ability to  the  flow  of  energons.  The  process  of  magnetiza- 
tion consists  in  an  axial  alignment  of  the  atoms  constituting 
the  substance.  We  regard  the  atom  as  composed  of  a  large 
number  of  sub-atomic  particles  playing  the  role  of  planets 
in  the  atomic  solar  system.  More  precisely,  we  may  think 
of  the  orbits  as  a  series  of  rings  or  loci  whose  planes  are 
parallel  to  each  other  and  perpendicular  to  a  common  polar 
axis  passing  through  the  ring  centers.  The  energons  con- 
tinuously rotate  during  their  passage  around  the  ring  loci 
orbits.  The  plane  of  an  energon  in  the  orbit  is  perpen- 
dicular to  the  ring  locus  tangent  at  every  point  in  the  locus. 
The  distance  between  the  rings  is  a  potential  function  of 
energy  of  the  rings.  In  other  words,  there  is  a  definite 
potential  difference  between  the  rings,  compatible  with  the 
maintenance  of  the  atom  as  a  comparatively  stable  struc- 
ture in  an  interacting  system.  This  is  also  true  of  all  sub- 
atomic groups  and  distances.  In  a  magnetized  substance 
the  polar  axes  of  the  atoms  have  been  aligned  and  energons 
may  therefore  invade  such  atoms  with  greater  ease  than  in  a 
non-magnetized  substance.  An  iron  disk,  in  the  presence 
of  a  magnet,  affects,  and  is  affected  by,  the  energonic  dis- 
placement in  the  atoms  of  the  magnet.  If  we  drop  a  body 
into  a  vessel  containing  water,  the  level  is  displaced.  Simi- 
larly by  introducing  a  piece  of  iron  into  the  field  surround- 
ing a  magnet  we  disturb  the  equilibrium  of  the  field.  The 


132  SCIENTIFIC  THEISM 

disturbance  of  the  equilibrium  is  equivalent  to  increasing 
the  stress  in  the  concurrent  system.  This  induces  polariza- 
tion of  the  atoms  constituting  the  iron  disk.  The  normal 
distance  between  energonic  rings  is  decreased,  due  to  the 
intrusion  of  the  iron  disk.  Furthermore,  some  of  the  ener- 
gonic rings  invade  the  now  polarized  iron,  thus  tending 
to  relieve  the  increased  stress  in  the  concurrent  system. 
The  tendency  to  relieve  the  congestion  is  concomitant  with  a 
further  decrease  in  the  ring  distance  which  is  equivalent  to 
shortening  the  axial  ring  line  through  magnet  and  iron 
disk.  This  is  accompanied  by  a  tendency  to  translate  the 
iron  disk  toward  the  magnet.  The  loci  of  the  energonic  ring 
centers  constitute  what  we  generally  mean  by  a  line  of  mag- 
netic force.  These  loci  are  merely  spatial  representations 
of  the  directional  resultants  of  interaction.  When  we  use  the 
term  "line  of  force"  we  mean  that  this  significance  only 
shall  be  attributed  to  it. 

From  electromagnetics  we  know  that  if  we  iook  along 
a  conductor  in  the  direction  in  which  the  current  is  flowing, 
the  lines  of  magnetic  force  around  the  conductor  are  in  a 
clockwise  direction.  This  means  that  the  energonic  rings 
travel  in  a  clockwise  manner  in  the  orbits  surrounding  the 
conductor.  While  their  centers  advance  along  the  lines  of 
force  (the  loci  of  the  moving  centers  constitute  the  lines  of 
force) ,  the  energons  themselves  rotate  in  a  clockwise  man- 
ner. For  a  reversal  in  the  current  direction  the  orbital 
motion  is  still  clockwise  in  reference  to  the  new  current 
direction.  This  orbital  direction  will  therefore  be  counter- 
clock-wise  in  reference  to  the  previous  rotation. 

The  effect  of  an  energy  increment  and  an  energy  decre- 
ment in  relation  to  the  potential  status  of  the  energon  must 
now  be  considered.  Physical  interaction  demands  that  the 
energon  be  capable  of  passing  through  three  phases  or 
states.  In  the  undisturbed  concurrent  system  the  phase  is 
neutral,  and  for  this  state  the  magnitude  of  the  intrinsic 
energy,  the  centrifugal  force,  and  the  radius  of  the  elemen- 
tary system  constitute  determinants  which  define  the 
energon  in  its  neutral  state.  In  fact,  in  the  neutral  phase 
the  term  "energon"  includes  these  determinants.  An  incre- 
ment of  energy  applied  to  the  energon  involves  an  increment 
in  the  determinants.  A  decrement  of  energy,  similarly,  in- 


SCIENTIFIC  THEISM  133 

volves  a  decrease  in  the  determinants  of  the  energon.  There 
is  a  maximum  and  a  minimum  limit  to  the  magnitude  of 
the  determinants,  corresponding  respectively  to  an  incre- 
ment and  a  decrement  of  energy.  The  energonic  system 
may  change  in  a  twofold  manner  from  its  neutral  condition. 
The  ascending  process  involves  a  definite  work  increment; 
the  descending  process  involves  an  equal  work  decrement. 
The  three  phases,  then,  may  be  designated  as  the  high,  neu- 
tral, and  low.  Passing  from  high  to  neutral  or  from  neutral 
to  low  is  a  descending  process  involving  compression.  If  the 
change  be  in  the  reverse  direction,  we  have  an  ascending 
process  which  involves  expansion.  The  ultimate  unit  of 
work  is  that  work  which  is  involved  in  the  change  in  phase 
of  the  energon  from  neutral  to  high  or  from  neutral  to  low, 
irrespective  of  the  direction  in  which  the  change  takes  place. 
The  three  phases  involve  two  steps  which  may  be  traversed 
in  either  direction.  Irrespective  of  direction,  each  step 
involves  the  same  amount  of  work.  The  ascending  and 
descending  processes  are  inseparable  in  all  phenomenal 
action.  The  development  of  an  ultimate  unit  of  work  incre- 
ment involves  the  compensating  appearance  of  an  ultimate 
unit  of  work  decrement.  The  energonic  reactions  therefore 
always  involve  a  pair  of  energons.  For  the  same  reason 
molecules  in  solution  are  broken  into  couples.  A  unit  of 
work  increment  applied  to  one  energon  involves  the  simul- 
taneous appearance  of  a  unit  of  work  decrement  in  another. 
The  work  expended  along  the  ascending  potential  gradient  is 
equal  to  the  work  stored  along  the  descending  potential 
gradient. 

In  the  high  phase  the  energon  becomes  an  electron.  In 
the  low  phase  the  energon  becomes  a  "positon."  The  word 
"positon"  indicates  that  the  energon  exists  in  that  phase 
which  is  the  extreme  of  the  electronic.  Moreover,  a  negative 
charge  is  always  associated  with  the  free  electron.  We  asso- 
ciate an  equal  positive  charge  with  the  positon.  In  the  last 
analysis  the  magnitude  of  this  negative  and  positive  charge 
depends  upon  the  work  increment  and  its  equivalent  work 
decrement.  Work  expended  is  always  equal  and  concomi- 
tant with  work  stored. 

Ions  in  solution  exhibit  these  three  phases  in  accordance 
with  the  precise  phase  change  in  the  energon.  In  other 


134  SCIENTIFIC  THEISM 

words,  the  phase  change  in  the  energon  is  the  factor  which 
determines  the  phase  of  the  ion.  Since  all  interaction  presup- 
poses the  concomitance  of  both  the  ascending  and  the  de- 
scending processes,  it  follows  that  the  products  of  solution 
must  appear  as  ionic  pairs.  An  odd  solution  component 
cannot  remain  in  solution.  In  this  we  have  the  real  reason 
why  molecules  break  down  into  so-called  "ionic  pairs."  We 
cannot  accept  that  contention  of  the  electrolytic  theory  of 
dissociation  which  holds  that  the  ionic  pairs  in  solution  are 
charged  in  an  opposite  electrical  manner. 

85.    The  Electric  Current  as  Transformed  Mechanical  Energy. 

Our  concurrent  system  model  is  now  sufficiently  com- 
plete to  test  its  usefulness  not  only  in  the  interpretation  of 
the  phenomena  connected  with  our  little  current  generator, 
but  also  in  the  elucidation  of  electrolytically  generated  cur- 
rents. The  author  has  also  applied  the  model  in  the  inter- 
pretation of  the  phenomenon  of  light.  These  applications 
of  our  model  are  discussed  later  in  the  text. 

Let  us  now  consider  what  happens  when  we  turn  the 
crank  of  our  generator.  It  is  evident  at  once  that  we  dis- 
turb the  energonic  axial  force  lines  the  moment  the  magnet 
is  rotated.  These  energonic  force  lines  form  closed  curves. 
The  energy  configuration  offers  resistance  to  the  disturb- 
ing influence.  The  work  done  by  the  material  group  is  of 
the  nature  of  an  ascending  process,  adding  energy  to  the 
electronic  groups,  which  expand  and  thus  become  electrons. 
For  every  electron  thus  formed  in  the  concurrent  system, 
involving  the  expenditure  of  an  ultimate  unit  of  work  incre- 
ment, an  energon  is  reduced  to  a  positon,  and  an  equivalent 
ultimate  work  unit  is  stored  in  the  positon.  Thus  we  have 
the  ascending  process  concomitant  with  the  descending 
process.  The  electron  can  again  become  a  neutral  energon 
by  having  an  ultimate  unit  of  work  done  upon  it.  Similarly, 
the  positon  can  give  up  its  stored  ultimate  work  unit  and 
again  become  a  neutral  energon.  Hence  work  can  be  done 
in  some  material  group  system.  The  elecron,  being  at  the 
high  phase,  can  do  no  more  work  within  certain  critical 
velocity  values,  and  it  may  therefore  be  regarded  as  nega- 
tive. The  positon,  however,  is  positive  in  its  ability  to  do 
work,  for  work  has  been  stored  in  its  production. 


SCIENTIFIC  THEISM  135 

As  the  energon,  due  to  the  influx  of  external  energy, 
becomes  an  electron,  the  surrounding  concurrent  system  is 
subjected  to  expansion.  Equilibrium  in  the  concurrent  sys- 
tem is  restored  by  the  formation  of  one  positon  for  every 
electron  generated.  The  equilibrium  within  the  magnet  itself 
is  disturbed.  As  an  energon  expands  into  an  electron  it  is 
displaced  out  of  the  magnet  into  the  concurrent  system. 
Simultaneously,  a  positon,  concomitantly  generated,  passes 
through  the  electron  into  the  magnet.  This  process  is  con- 
tinuous while  energy  is  expended  in  turning  the  crank  of 
the  machine.  A  stream  of  electrons  moves  along  the  new 
resultant  force  lines  into  the  iron  disk  and  thence  into  the 
conducting  wire  and  the  external  circuit.  Simultaneously, 
a  stream  of  positons  moves,  at  the  same  rate,  in  the  opposite 
direction  through  the  magnet  and  into  the  external  circuit 
by  way  of  the  conductor.  The  positon  is  ready  to  give  up 
its  stored  work  to  the  external  system  and  thus  become 
once  more  an  energon.  At  the  same  time  an  equal  amount 
of  work  is  done  upon  the  electron  by  the  external  system 
transforming  it  also  into  an  energon.  The  little  current  gen- 
erator is  therefore  an  energy  transformer.  It  manufactures 
electrons  and  positons  out  of  energons. 

86.     Primary  and  Secondary  Matter  in  the  Role  of  Concurrent 

and  Excitant  Systems. 

Primary  matter  may,  then,  be  regarded  as  activity 
groups  arranged  in  conformity  with  the  demands  of  inter- 
action. The  definite  locations  and  phases  of  action  of  these 
centers  depend  upon  the  magnitude  of  the  interaction  at  any 
given  moment  of  time.  Space,  then,  is  merely  a  chart  of 
apprehension  which  gives  only  relative  meaning  to  activity 
manifestations.  This  also  is  true  of  time.  Instead  of  space 
being  a  genuine  reality  which  isolates  the  centers  from  each 
other  and  thus  constitutes  a  barrier  to  physical  action, 
space  is  merely  a  relative  interpreter  of  the  intensity  of  the 
interaction.  Since  the  energy  phase  is  our  broadest  physical 
concept  pertaining  to  the  activity  content,  we  may  think  of 
these  activity  centers  as  localized  energy.  However,  local- 
ized energy  does  not  mean  that  the  activity  of  these  centers 
is  accounted  for  by  the  mere  word  "energy,"  because  the 
word  "energy"  signifies  only  a  phase  of  that  activity  which 


136  SCIENTIFIC  THEISM 

owes  its  beginning  and  maintenance  to  God  the  Creator. 
Secondary  or  normal  matter  is  merely  transformed  pri- 
mary matter.  In  certain  phenomena  the  elementals  of  sec- 
ondary matter,  like  the  electron,  serve  as  excitant  systems, 
which,  in  conjunction  with  the  concurrent  system,  account 
for  such  manifestations  as  the  phenomena  of  light  and 
electricity. 

87.  Space  Not  Unreal. 

Space  is  not  a  thing.  Thought  is  not  a  thing.  It  does 
not  follow  that,  because  space  and  thought  are  not  things, 
both  have  no  reality.  Because  space  is  a  form  of  finite 
apprehension,  it  does  not  follow  that  space  is  unreal.  Like 
other  types  of  finite  reality,  space  is  not  independent.  It  is 
a  form  interdependent  with  reality.  Space  arises,  as  it 
were,  out  of  interaction.  As  a  form  of  apprehension  or 
awareness  it  pertains  to  the  knowing  and  perceiving  con- 
scious subject.  Objectively  it  finds  its  significance  in  the 
interdependent  activities  manifest  in  the  physical  universe. 
Psychologically,  the  space  form  is  a  temporal  genesis. 
Because  of  the  fact  of  interaction  between  subject  and 
object,  the  space  form  is  general  and  not  particular,  and 
an  a  priori  science  of  geometry  is  possible.  Space  is  not 
an  X  which  holds  things  in  definite  positions  and  keeps  them 
either  together  or  apart.  The  apartness  and  nearness  of 
things  are  due,  on  the  contrary,  to  an  interdependent  inter- 
action. The  separateness  of  things  is  due  to  the  activity  of 
things,  and  its  magnitude  is  measured  in  spatial  terms.  We 
apprehend  this  separateness  in  terms  of  the  space  form  and 
measure  its  magnitude  in  terms  of  distance. 

88.  Extension. 

Since  the  space  forms  originate  in  interaction,  the  occu- 
pation of  space  is  due  primarily  to  the  activity  of  things. 
The  "how  much?"  of  space  occupation  is  answered  by  the 
"this  much"  of  activity.  Extension,  therefore,  is  a  form  of 
action.  It  is  a  "this  much"  of  action.  Extension,  however, 
is  only  one  of  many  ways  of  measuring  the  amount  or  mag- 
nitude of  an  action.  Consequently,  it  is  merely  one  phase 
of  activity. 


SCIENTIFIC  THEISM  137 

89.  Primary  and  Secondary  Causes. 

Reality  is  ultimately  divided  into  an  Absolute  Reality 
and  a  relative  reality,  God  and  His  created  cosmos.  In  the 
rationally  ordered  physical  universe  the  relationships  be- 
tween its  members  are  intelligible  in  terms  of  space,  time, 
and  causation.  The  physical  universe  is  a  complete  unitary 
system  which  differentiates  itself  into  a  temporal  series  of 
events  appearing  as  antecedents  and  consequents.  Causes 
and  effects  as  known  in  the  complete  relativity  system  of 
the  cosmos  constitute  what  we  have  previously  designated 
as  secondary  causes.  The  universe  of  physical  action  is 
causal  and  deterministic.  The  physical  world  is  a  world  of 
uniformities  and  natural  laws.  The  secondary  causes  are 
describable  in  terms  of  natural  laws.  Our  own  conscious 
activity  is  non-causal  in  the  sense  of  natural  law.  We  origi- 
nate, and  consequently  our  activity  is  in  the  nature  of  a 
"free  cause."  Our  freedom  is  exercised  within  the  limits  of 
a  causal  and  deterministic  world  order.  The  freedom  of 
the  Absolute  is  above  these  limitations.  God's  freedom  is 
beyond  the  realm  of  secondary  causation.  Cause  and  effect 
in  the  sense  of  secondary  causation  are  of  God  but  not  in 
God.  We  originate  in  a  world  of  restrictions  and  limita- 
tions. Consequently  our  originations  are  of  relative  value 
and  meaning.  Our  free  originations  and  acts  are  brought 
into  conformity  with  the  deterministic  mandates  of  environ- 
ment by  the  inflexible  coercion  of  experience.  God's  origi- 
nation is  Absolute  and  above  all  limitations.  Our  freedom  is 
like  God's,  but  only  in  part.  An  act  or  origination  is  our 
own  free  act,  but  its  form  is  limited  by  the  deterministic 
order  of  the  physical  universe.  God's  origination  is  free  in 
an  Absolute  sense  because  it  is  above  the  unitary  relativity 
system.  God's  free  origination  is  therefore  the  only  true 
primary  causation.  The  being  of  God  is  a  Transcendent 
Being  free  from  the  limits  of  relativity.  We  attribute  the 
creation  of  the  cosmos  to  the  primary  causation  of  God. 

90.  Physical  Proof  of  the  Transcendence  of  God. 

The  interpretation  of  the  physical  universe  as  a  unitary 
relativity  system  results  in  an  inert  mechanical  model.  If 
we  think  of  the  physical  universe  as  a  fragment  of  a  great 
all,  unknown  in  part,  then  we  have  pantheism.  If  we  con- 


138  SCIENTIFIC  THEISM 

aider  the  universe  as  created  by,  but  independent  of,  God 
then  we  have  deism.  Contemplating  the  world  as  a  self- 
sufficient  given,  self-operative,  and  uncreated  Godless  sys- 
tem, we  arrive  at  the  position  of  materialism  or  atheism. 
Deism,  atheism,  and  pantheism  involve  an  inert  mechanical 
model  despite  the  supposed  differences  in  the  three  positions. 
We  have  shown  in  paragraph  24  that  the  ultimate  poten- 
tial difference  in  the  physical  universe  is  maintained  by 
God.  Consequently  the  positions  of  deism  and  atheism  are 
both  untenable.  Pantheism  is  merely  deism  raised  to  the 
nth  power;  it  is  an  all-inclusive  deism.  The  pantheistic 
"all"  is  no  more  maintainable  within  itself  than  the  deistic 
or  atheistic  universe.  The  physical  model  of  the  pantheist 
is  just  as  inert  and  inoperative  as  the  deistic  and  atheistic 
model.  It  follows  that  a  Being  must  exist  independently  of 
the  physical  universe,  upon  whom  the  cosmos  depends  for 
its  continuous  existence.  Thus  we  arrive  at  a  proof  of  the 
Transcendence  of  God. 

91.     Transcendence  and  Immanence. 

It  may  be  maintained  that  we  have  arrived  at  a  repul- 
sive dualism.  We  contend  that  the  mere  word  "dualism" 
is  no  more  repugnant  than  the  word  "monism."  Incon- 
sistency is  the  only  justifiable  cause  of  intellectual  repug- 
nancy. The  objection  may  be  raised  that  we  have  divided 
the  totality  of  reality  T  into  two  parts,  A,  the  Absolute 
Reality  of  God,  and  S  the  cosmic  reality  of  the  unitary  rela- 
tivity system.  The  relation,  expressed  mathematically, 
takes  the  form 

T  =  A+S  =  A+/{a,  b,  c, R}  =  A+/|Unity}. 

The  unity  of  all  reality  established  by  the  pantheist  and 
the  monist  is  merely  a  unity  of  multiplicity.  The  unity  of  the 
physical  universe  which  we  hold  as  a  fundamental  truth  is 
a  unity  of  multiplicity.  The  unity  of  the  conscious  self  is 
a  unity  of  conscious  states.  The  unity  of  the  monon  is  a 
unity  of  numerous  phases,  states,  and  qualities  constituting 
a  physical  character  content.  Therefore  all  forms  of  reality 
exhibit  a  unity  which  is  unintelligible  without  multiplicity. 
A  unity  which  does  not  partake  of  multiplicity  is  merely  a 
mathematical  abstraction  having  no  other  significance.  A 


SCIENTIFIC  THEISM  139 

real  unity,  possessing  a  content,  consequently  is  not  a  mere 
mathematical  abstraction.  Relatedness  is  the  norm  of 
unity.  It  is  evident  that  the  very  idea  conveyed  by  the 
term  "relatedness"  suggests  multiplicity.  The  relatedness 
between  mere  numbers  is  nothing  more  than  a  mathematical 
abstraction.  The  type  of  the  unity  depends  upon  the  kind 
of  relatedness.  We  draw  a  sharp  distinction  between  unity 
and  identity.  God  and  His  created  world  are  not  identities. 
A  relationship  exists  between  God  and  the  cosmos.  It  does 
not  therefore  follow  that  the  cosmos  and  God  are  identical. 
Immanence  and  transcendence  constitute  the  form  of  the 
relatedness  between  God  and  the  world.  This  type  of  related- 
ness  defines  the  form  of  the  unity  existing  between  the 
Divine  Being  and  His  created  world.  This  type  of  unity  does 
not  signify  identity.  In  the  physical  universe  thing  A  is  not 
identical  with  thing  B.  Nevertheless  a  relationship  exists 
between  thing  A  and  thing  B  as  well  as  between  things  A 
and  B  and  the  rest  of  the  physical  universe.  Thing  A  is 
not  therefore  identical  with  thing  B  nor  with  the  remaining 
things  in  the  universe.  God  is  not  isolated  from  His  created 
world.  We  have  seen  that  ultimately  the  physical  universe 
depends  upon  God  for  its  continuous  maintenance.  God  is 
the  prime  and  ultimate  sustaining  cause  of  the  physical  uni- 
verse. In  the  cosmos  the  imprint  of  God's  Omnipotence  and 
Omniscience  is  seen  in  secondary  causation  which  guaran- 
tees order  and  uniformity  in  the  physical  universe.  How- 
ever, mere  secondary  causation  is  incapable  of  rendering 
the  world  intelligible.  God  must  also  be  Transcendent,  but 
not  isolated  from  the  universe.  We  have  fathomed  but  a 
fragment  of  the  causal  nexus.  The  ultimate  relationship 
between  God  and  the  universe  is  and  ever  will  be  a  mystery 
to  finite  consciousness.  Nevertheless,  a  real  relationship 
must  exist  if  we  hope  to  interpret  even  a  mere  fragmentary 
portion  of  God's  created  work.  Since  God  is  not  isolated 
from  the  universe,  He  may  reveal  Himself  in  time  in  a  man- 
ner inexplicable  to  finite  consciousness  because  of  our  lim- 
ited and  finite  understanding  of  the  profundities  of  the  rela- 
tionships which  manifest  in  the  cosmos.  Because  of  our 
finiteness  these  Revelations  may  appear  as  nodes  in  the  cas- 
ual nexus.  Because  of  our  limited  knowledge  these  nodes 
may  be  inexplicable  in  terms  of  uniformity.  If  this  world 


140  SCIENTIFIC  THEISM 

is  nothing  more  than  a  machine,  then  uniformity  is  absolute. 
If  our  conscious  life  is  merely  mechanical,  then  free  origi- 
nation is  impossible.  Our  conscious  life  is  more  than  mere 
mechanism,  consequently  nodes  of  origination  are  possible. 
It  does  not  follow  that  these  nodes  are  therefore  irrational. 
A  nodal  conscious  life  may  upset  the  traditions  of  uni- 
formity because  of  a  deeper  and  more  profound  system  of 
relationships.  From  the  standpoint  of  uniformity,  the  in- 
ventive achievements  of  conscious  life  may  appear  to  be 
miraculous.  Since  God  is  not  estranged  from  the  universe, 
His  temporal  revelations  may  appear  as  miraculous  nodes 
when  compared  with  physical  uniformity.  The  mathe- 
matical law  of  a  curve  may  include  nodal  points  which 
break  in,  as  it  were,  upon  the  general  uniformity.  For  this 
reason  the  nodes  are  not  unreal.  From  the  Infinite  view- 
point the  revelations  acquire  a  relatedness  to  the  world 
order  of  deeper  significance  than  mere  mechanical  uniform- 
ity. Since  God  is  not  isolated  from  the  world,  but  is  Imma- 
nent in  it,  His  primary  causation  may  deflect  the  general 
uniformities  of  secondary  causation  into  nodes  inexplic- 
able to  our  limited,  finite  knowledge  of  the  physical  causal 
nexus.  Such  deflections,  however,  are  in  complete  harmony 
with  the  deeper  significance  of  reality.  They  are  a  fuller 
and  more  complete  expression  of  reality  in  its  ultimate 
meaning,  and  as  such  are  in  full  accord  with  the  principle  of 
non-contradiction  which  unifies  both  primary  and  secondary 
causation.  God,  the  Absolute,  is  the  Infinite  Perfection 
inspiring  the  imperfect.  God  is  the  unity  of  all  truth.  The 
fundamental  characteristic  of  the  Being  of  God  is  non-con- 
tradiction. The  principle  of  non-contradiction  actuates  the 
physical  universe  and  unifies  primary  and  secondary  cau- 
sation. The  general  physical  uniformities,  known  as  nat- 
ural laws,  are  fragmentary  expressions  of  the  all-inclusive 
principle  of  non-contradiction  which  demands  the  Imma- 
nent activity  of  God  in  such  revelations  as  insure  the  realiza- 
tion of  purpose  and  teleology  in  His  created  universe.  These 
revelations  are  in  strict  conformity  with  the  principle  of 
non-contradiction  which  is  the  essence  of  the  Being  of  God. 
When  viewed  from  the  standpoint  of  the  fragmentary  nat- 
ural laws  these  revelations  may  appear  as  miracles,  but 
from  the  standpoint  of  the  all-inclusive  principle  of  non- 


SCIENTIFIC  THEISM  141 

contradiction  they  complete  and  harmonize  the  intent  of 
reality.  It  should  be  evident  that  our  position  differentiates 
itself  in  a  marked  manner  from  the  pantheistic,  monistic, 
deistic  and  atheistic  positions.  In  order  that  the  distinction 
may  be  readily  apparent,  we  resort  to  the  shorthand  of 
mathematics.  In  the  above  we  have  represented  the  totality 
of  reality  T  by  the  following  expression : 

T=A+S 

in  which  A  is  the  Absolute  Reality  of  God,  and  S  is  the 
reality  of  the  cosmos.  The  various  positions  mentioned 
above  may  be  represented  as  follows : 

I.  Pantheism. 

T=A=S. 

The  totality  T  is  identical  and  equal  to  the  reality  of  God, 
or  it  is  equal  and  identical  with  the  cosmos.  In  other  words, 
the  cosmos  and  God  are  identical.  The  fallacy  of  this  posi- 
tion has  been  pointed  out  in  the  preceding. 

II.  Monism. 

T=A=S. 

This  formula  is  the  same  as  for  the  pantheistic  position. 
The  monist  may  try  to  deny  that  he  is  a  pantheist.  With 
subtle  verbosity  he  may  try  to  create  a  distinction,  but  in 
the  last  analysis  his  formula  reduces  to  the  pantheistic. 
Monism  is  nothing  more  than  a  modernized  pantheism. 

III.  Deism. 

T=A+S. 

The  totality  of  reality  T  is  divided  into  two  distinct  and 
independent  parts ;  that  is,  the  Absolute  A  and  the  cosmos 
S,  created  by  God  but  independent  of  God.  The  cosmos  is 
sufficient  unto  itself  and  does  not  need  the  existence  of 
God  for  its  maintenance.  The  fallacy  of  this  position  has 
already  been  noted.  If  S  is  merged  into  A,  or  A  into  S, 
then  the  deistic  position  becomes  identical  with  pantheism 
or  monism. 


142  SCIENTIFIC  THEISM 

IV.  Atheism  or  Materialism. 

T=S. 

The  totality  of  reality  consists  of  the  cosmos  only. 
There  is  no  God.  All  is  mere  matter  and  energy.  This  is 
the  fallacious  position  of  atheism  and  materialism. 

It  is  clearly  evident  that  pantheism,  monism,  and  athe- 
ism, in  the  last  analysis,  are  practically  identical  positions. 
There  can  be  very  little  real  distinction  between  the  two 
statements,  (1)  that  God  is  the  cosmos,  and  (2)  that  the 
cosmos  is  the  only  existing  God.  Such  apparent  distinctions 
as  are  drawn  are  mere  subtle  sophistries.  A  mechanical 
model  constructed  upon  the  above  outlined  positions  is  inop- 
erative. Deism  fails  totally  in  this  respect  because  of  its 
absolute  isolation  of  God  and  the  cosmos. 

The  results  of  scientific  research,  when  properly  inter- 
preted, therefore  force  us  to  the  theistic  position  as  the 
only  philosophical  system  which  conforms  with  the  results 
of  the  scientific  method.  The  facts  of  science,  when  driven 
to  consistent  conclusions,  force  us  beyond  the  relativity  sys- 
tem of  the  physical  universe  to  the  Being  of  God  in  accord- 
ance with  the  philosophy  of  theism. 

V.  Scientific  Theism. 

T=A+/(a). 

In  the  philosophy  of  Scientific  Theism  we  look  upon  the 
totality  of  reality  as  consisting  of  the  Absolute  Reality  of 
God,  A  and  the  dependent  cosmos  a.  The  cosmos  a  is  of  God 
through  the  act  of  creation,  but  it  is  not  God.  Nevertheless, 
the  cosmos  a  depends  continuously  upon  God  for  its  main- 
tenance ;  hence  we  may  say  mathematically  that  a,  the  cos- 
mos, is  a  function  /  (a)  of  God.  In  this  manner  we  repre- 
sent, in  the  shorthand  of  mathematics,  the  truth  of  both 
Transcendence  and  Immanence.  The  principle  of  non-con- 
tradiction is  of  the  Being  of  God  and  in  the  being  of  the 
cosmos,  first,  through  His  act  of  creation,  and,  second, 
through  His  Immanence  and  Revelation.  Primary  free 
causation  and  secondary  causation  are  harmonized  in  the 
all-inclusive  principle  of  non-contradiction.  The  principle 
of  non-contradiction  manifests  purposively  and  teleologi- 
cally  in  the  universe. 


SCIENTIFIC  THEISM  143 

92.     Purpose  and  Teleology. 

Mechanism  and  natural  law  in  the  sense  in  which  we  have 
defined  them  are  compatible  with  spontaneity,  individuality, 
purpose,  and  teleology.  As  a  mere  machine  the  cosmos  is 
inert,  and  there  is  no  room  for  spontaneity  and  teleology. 
Uniformity  means  that  every  change  is  understandable  as 
a  variation  in  a  rational  system.  Purpose  implies  that  there 
are  further  adjustments  necessary,  more  contradictions 
which  must  be  resolved  before  harmonic  relations  with 
reality  can  be  established.  A  purpose  is  right  only  in  so 
far  as  it  is  in  harmony  with  reality.  The  realization  of  a 
purpose  means  that  conditions  have  been  brought  into  con- 
formity with  the  divine  principle  of  non-contradiction.  Con- 
sequently we  may  say  that  purpose  is  the  intent  of  reality 
deferred  in  time.  As  far  as  the  finite  mind  is  concerned, 
purpose  is  no  guarantee  of  value.  When  we  have  a  vision 
of  the  whole,  then  we  can  discern  the  ideal  which  shapes 
the  future.  The  future  content  is  the  result  of  the  working 
of  the  ideal.  The  accidental  is  given  fundamental  impor- 
tance in  modern  scientific  thought.  According  to  this  hy- 
pothesis, a  plant  is  an  accidental  by-product  of  the  activities 
of  elements  which  contained  nothing  in  their  individual 
nature  or  in  their  relationships  that  involved  the  slightest 
certainty  that  a  plant  would  evolve.  Such  an  hypothesis 
verges  on  the  ridiculous  and  makes  knowledge  impossible. 
There  is  no  valid  reason  why  the  accident  hypothesis  should 
be  applied  to  the  organic  world  only.  If  it  is  true,  then  it 
would  be  difficult  indeed  to  assign  a  reason  why  it  is  not 
equally  true  in  the  inorganic  world.  From  another  stand- 
point, if  there  is  some  form  of  teleology  assignable  to 
organic  phenomena,  then  that  same  form  must  be  inclusive 
of  inorganic  and  conscious  phenomena.  There  must  be 
teleology  below,  in,  and  above  consciousness.  The  mathe- 
matical probability  that  accident  could  have  brought  about  a 
cosmos  is  nil.  Accident  is  the  father  of  chaos,  and  intelli- 
gent, productive  relationship  is  the  father  of  cosmos.  What 
we  do  find  in  the  world  is  an  unfoldment  of  an  immanent 
reality.  The  plan  of  the  plant  was  immanent  in  the  entire 
and  complete  interaction  of  the  universe.  The  plant  did  its 
part,  environment  did  the  rest,  and  between  both  there  ex- 
isted that  perfect  understanding  which  only  God  could  give 


144  SCIENTIFIC  THEISM 

to  His  created  cosmos.  The  molding  of  the  structure  of 
the  body  or  organism  in  the  earlier  phases  of  development 
cannot  be  ascribed  to  an  inherent  conscious  knowledge  exist- 
ing in  the  earlier  phases;  it  must  rather  be  sought  in  the 
deeper  inherent  and  hidden  God-given  endowment  of  the 
environment. 

The  great  movements  of  civilization,  the  development  of 
religions,  of  ideas,  and  of  art  find  no  counterpart  in  a  plan 
existing  in  a  finite  mind.  Finite  consciousness  plays  its  part 
in  the  deposition  of  the  strata  of  civilization,  but  no  finite 
mind  ever  grasped  the  significance  of  the  grand  totality,  and 
consequently,  as  far  as  the  great  movements  are  concerned, 
finite  mind  is  unconscious  of  the  intricacies  and  multiplicity 
of  its  ramifications.  There  is  intelligence  in  every  step,  but 
it  is  of  an  immanent  order  hidden  deeper  in  the  mystery  of 
things  than  finite  eye  can  perceive.  This  immanence  points 
clearly  to  a  Being  Transcenednt  and  above  the  physical 
order.  Without  Transcendence  this  immanence  is  inexplic- 
able. The  great  movements  are  typical  of  a  teleology  above 
consciousness.  In  this  we  have  another  proof  of  God's 
Transcendence.  Teleology  finds  its  real  meaning  in  indi- 
viduality and  completeness,  which  constitute  the  supreme 
essence  of  cosmic  value,  and  as  a  finite  conscious  striving 
it  is  a  temporal  desire  for  harmony  with  reality.  In  this 
manner,  then,  does  the  principle  of  non-contradiction  force 
imperfection  toward  perfection  along  the  stream  of  contra- 
diction and  unrest. 


CHAPTER  VI 
NON-NEWTONIAN  DYNAMICS 

93.     The  True  Relation  Between  Statics  and  Dynamics. 

If  we  regard  space  as  a  chart  of  potential  values,  then 
the  behavior  of  a  particle  or  mass  aggregate  is  determined 
by  its  own  work  value  interacting  with  the  other  work 
values  in  the  field.  Space,  then,  is  a  field  of  activity  values. 
Interaction  between  activity  centers  is  describable  in  terms 
of  the  dynamics  of  motion.  For  purposes  of  analysis  we 
may  set  up  an  instantaneous  dynamics  which  then  becomes 
our  only  true  statics.  The  hypothetical  cessation  of  activity 
and  the  recording  of  the  instantaneous  activity  tendencies 
which  obtain  at  any  particular  instant  constitute  what  we 
call  statics.  When  we  equilibrate  the  instantaneous  ten- 
dencies by  the  introduction  of  suitable  factors,  then  we 
have  cases  of  ordinary  statics  as  met  with  in  the  science 
of  mechanics.  These  instantaneous  activity  tendencies  may 
be  conveniently  considered  as  stresses  in  the  interaction 
fields.  A  particle  when  unrestrained  by  the  hypothetical 
cessation  of  interaction,  upon  the  removal  of  the  hypotheti- 
cal restriction  will  be  displaced  in  complete  accord  with  the 
deduced  instantaneous  activity  tendencies.  It  will  move 
with  definite  velocity  in  that  particular  path  which  the  inter- 
acting activity  tendencies  dictate.  From  our  viewpoint 
statics  is  an  instantaneous  and  consequently  hypothetical 
or  potential  dynamics.  Statics  is  dynamics  viewed  from  the 
hypothetical  limiting  case  of  arrested  motion  or  zero  veloci- 
ties. Statics  is  an  analytical  convenience  by  means  of  which 
the  future  behavior  of  a  system  may  be  predicted.  Mathe- 
matics is  neither  statical  nor  dynamical.  The  mere  inser- 
tion of  the  letter  V,  meaning  velocity,  and  the  letter  A,  indi- 
cating acceleration,  does  not  create  dynamics  out  of  mathe- 
matics. If  activity  were  not  the  essense  of  reality,  then 
mathematics  could  not  be  a  means  of  representing  dynami- 
cal relations.  Conversely,  since  activity  is  the  essence  of 

145 


146  SCIENTIFIC  THEISM 

reality,  it  follows  that  the  introduction  of  instantaneous 
statics  does  not  cause  the  cessation  of  dynamical  activity. 
Therefore  we  may  pass  from  instantaneous  statical  rela- 
tions to  dynamical  relations,  with  the  certainty  that  we  are 
not  violating  the  true  principles  of  dynamical  activity.  Con- 
sequently if  we  have  investigated  the  instantaneous,  and 
therefore  statical,  conditions  of  a  plane  in  space,  we  have 
correctly  ascertained  the  conditions  governing  the  subse- 
quent motion  of  any  particular  system  assigned  to  the  plane. 
For  these  reasons  we  reserve  the  right  to  proceed  in  this 
manner  whenever  the  requirement  of  a  particular  analysis 
demands  the  use  of  this  method.  Moreover,  since  space  is 
a  chart  of  potential  or  work  values,  the  investigation  of  the 
instantaneous  conditions  in  a  field  enables  us  to  develop  the 
dynamics  of  a  system  in  conformity  with  what  we  may  term 
the  stress  conditions  of  the  field.  By  stress  conditions  in  a 
field  or  plane  we  mean  the  instantaneous  activity  condi- 
tions tending  to  the  production  of  motion.  The  curvilinear 
or  rectilinear  resultant  arising  from  such  an  investigation 
constitutes  the  resultant  path  of  motion  of  the  system  as- 
signed to  the  field.  The  true  relation  between  statics  and 
dynamics  is  therefore  emphasized  in  the  Space-Time  Poten- 
tial. Since  every  relative  point  in  space  has  a  relative  work 
value,  our  system  is  fundamentally  dynamical.  The 
dynamics  of  the  Space-Time  Potential  is  essentially  Non- 
Newtonian. 

94.     Non-Newtonian   Dynamics. 

We  retain  in  our  Non-Newtonian  Dynamics  the  funda- 
mental relations  pertaining  to  motion,  force,  and  work.  For 
reasons  given  later  we  abandon  the  Newtonian  relation 

(  j2  J  and  adopt  its  anti-differential,  that  is,  /  ^-f  be- 
cause of  its  direct  relation  to  the  fundamental  relations 
pertaining  to  motion,  force,  and  work.  Moreover,  we  sub- 
stitute the  anti-differential  because  of  the  fact  that  it  makes 
possible  a  complete  unification  of  statics,  dynamics,  atomic 
dynamics,  ultra-atomic  dynamics,  thermodynamics,  the 
theory  of  light  and  electricity.  The  innovation  is  justified 
not  alone  by  the  resulting  unification  and  simplification,  but 


SCIENTIFIC  THEISM  147 

by  the  fact  that  our  system  becomes  philosophically  defen- 
sible and  consistent.  In  our  Non-Newtonian  Dynamics  we 
require  no  constants  to  bridge  the  discrepancies  between 
ultra-atomic  dynamics  and  the  dynamics  of  material  aggre- 
gates. The  observed  relations  of  physical  astronomy  are 
derived  from  the  Newtonian  relation  by  resorting  to  un- 
justifiable limitations.  Without  these  unjustifiable  limita- 
tions, Newton  could  not  have  derived  the  Keplerian  Laws. 
Coulomb's  relation  is  subject  to  the  same  criticism.  The  uni- 
versality of  the  Newtonian  relation  must  be  abrogated 
whenever  we  desire  to  apply  it  to  a  definite  system. 

95.     Critical  Analysis  of  the  Newtonian  Relation. 

The  Newtonian  deductions  concerning  planetary  motion 
depend  upon  the  fundamental  assumption  that  the  distance 
s  between  two  centers  (sun  and  earth,  for  example)  varies ; 
then  it  is  shown  that  the  type  of  the  orbits  (conic  sections) 
depends  upon  the  special  form  of  the  expression  for  velocity. 
Now  if  the  distance  s  varies  in  a  given  time,  then  naturally 
the  velocity  must  vary.  Since  a  mass  variation  is  excluded 
in  the  assumption  upon  alleged  physical  grounds,  it  is  main- 
tained that  the  phenomenon  is  solely  due  to  a  distance  vari- 
ation. The  masses  of  both  the  earth  and  the  sun  are  sup- 
posed to  remain  constant,  hence  the  distance  variation  is 
the  only  condition  which  affects  the  problem.  If  the  dis- 
tance s  did  not  vary,  the  application  of  the  differential  cal- 
culus would  produce  a  result  equal  to  zero,  for  the  differ- 
ential coefficient  of  a  constant  is  zero.  The  retort  is  that  the 
distance  s  actually  does  vary,  hence  we  have  the  right  to 
apply  the  differential  calculus  to  the  problem.  We  admit 
that  astronomical  observations  show  conclusively  that  the 
variation  in  the  distance  s  takes  place,  but  we  contend  that 
the  calculus  creates  no  physical  reason  for  the  variation. 
All  that  we  get  out  of  the  procedure  is  the  fact  that  if  there 
is  a  variation  in  the  distance  s,  then  there  is  a  variation  in 
the  velocity  of  the  planetary  body  and  the  type  of  the  orbit 
depends  upon  the  nature  of  the  velocity  variation.  This  in 
itself  is  nothing  astounding.  A  layman,  not  conversant  with 
the  calculus,  would  arrive  at  the  same  conclusion.  The 
crux  of  the  problem  is  in  the  variation  of  s,  the  distance 
between  the  central  body  and  its  satellite.  The  following 


148  SCIENTIFIC  THEISM 

question  is  here  pertinent :  Is  the  change  in  velocity  of  the 
satellite  due  to  a  change  in  the  distance  s,  or  is  the  change 
in  the  distance  s  due  to  a  change  in  the  velocity  of  the  satel- 
lite ?  It  may  be  replied  that  our  question  is  a  mere  trick  of 
sophistry  and  that  the  fact  is  that  the  satellite  arrives 
within  the  sphere  of  influence  of  the  central  body  with 
a  definite  initial  velocity.  After  this  arrival,  the  gov- 
erning influence  of  the  central  body  begins.  We  main- 
tain that  this  reply  evades  the  question.  Moreover,  we 
hold  that  the  question  is  pertinent.  The  reply  suggests 
another  question.  Where  does  the  sphere  of  influence  of 
the  central  body  begin,  and  when  may  we  state  that  the 
satellite  has  "arrived"?  According  to  Newton,  the  grav- 
itational effect  extends  throughout  the  universe  ad  infinitum. 
The  line  of  demarcation  which  bounds  the  sphere  of  influ- 
ence of  the  central  body  must  consequently  be  coincident 
with  the  resultant  locus  arising  from  the  mutual  action 
between  the  central  body  and  the  remaining  totality  of  the 
universe.  It  is  assumed  that  the  mass  of  the  central  body 
remains  constant.  Therefore  the  behavior  of  the  satellite 
when  it  reaches  this  line  of  demarcation  must  be  governed 
by  the  conditions  which  pertain  to  the  remaining  totally  of 
the  universe.  The  mutual  action  between  the  central  body 
and  the  rest  of  the  universe  defines  the  locus  of  demarcation, 
but  since  the  central  mass  is  constant  the  subsequent  be- 
havior of  the  satellite  depends  upon  the  rest  of  the  universe. 
It  is  evident  that  the  governing  conditions  in  the  rest  of  the 
cosmos  may  be  of  a  constant  or  a  variable  nature.  If  they 
are  constant,  then  the  locus  resultant  must  depict  a  path 
conformable  with  a  constant  velocity,  that  is,  a  circle.  If 
the  governing  conditions  in  the  rest  of  the  physical  universe 
persist  in  variability,  then  the  locus  will  be  a  curve  which 
conforms  with  this  variation.  If  the  variation  is  pulsating 
and  periodic,  then  the  locus  may  be  a  conic  of  the  elliptic 
form.  The  variation  in  the  rest  of  the  universe  may  involve 
changes  in  position  or  mass  magniture,  or  both.  The  initi- 
ation of  this  variation  cannot  be  ascribed  to  anything  or  any 
source  within  the  system  itself.  It  must  be  due  to  an  agency 
outside  of  the  system.  Consequently  the  Newtonian  impli- 
cations force  us  to  the  concept  of  a  Transcendent  God.  If 
resort  is  made  to  an  infinite  time,  then  the  variations  in 


SCIENTIFIC  THEISM  149 

the  rest  of  the  universe  would  long  ago  have  ceased.  The 
cosmic  system  would  then  have  had  an  infinite  time  within 
which  to  equilibrate  itself.  The  clock  of  the  universe  cannot 
wind  itself,  for  there  is  no  perpetual  motion  extant  within 
the  universe.  Continuous  activity  ultimately  depends  upon 
the  continuous  maintenance  of  a  potential  difference  within 
the  physical  universe.  We  have  already  proved  that  God 
only  can  maintain  this  potential  difference.  Returning  to 
the  question  concerning  the  relation  between  a  change  in 
the  distance  s  and  the  change  in  velocity,  we  realize  fully 
that  the  form  of  the  question  is  repulsive  to  the  physicist. 
He  will  maintain  that  the  change  in  velocity  inevitably 
involves  a  change  in  s,  the  distance,  and  conversely  that  a 
change  or  variation  in  the  distance  s  with  equal  certainty 
involves  a  variation  in  the  velocity.  We  hold  that  this  con- 
tention of  the  physicist  is  a  sophism  par  excellence.  Most 
assuredly  the  contention  is  true  because  it  is  a  mere  state- 
ment of  identity.  Nothing  is  contained  in  the  one  idea  that 
is  not  already  contained  in  the  other.  If  the  distance  s 
varies,  then  the  velocity  varies;  and  if  the  velocity  varies, 
then  s,  the  distance,  varies.  The  intent  of  our  question  is 
to  discover  the  nature  of  the  potent  condition  which  is 
capable  of  bringing  about  a  change  or  variation  in  either 
the  distance  s  or  the  velocity  of  the  satellite.  No  one  will 
maintain  that  the  distance  s  is  a  potent  agency  which  is 
capable  of  changing  itself  to  something  other  than  itself. 
It  follows  that  the  change  in  the  distance  s  is  a  mere  accom- 
paniment, though  inevitable,  of  the  variation  in  the  velocity. 
We  have  seen  that  the  masses  of  the  central  body  and  the 
satellite  have  nothing  to  do  with  the  variation  because  they 
are  constant.  Be  it  understood  that  this  is  the  Newtonian 
position.  From  our  viewpoint  these  two  masses  interact 
with  the  rest  of  the  universe,  and  therefore,  whether  con- 
stant or  variable,  they  are  not  impotent  factors  in  the  phe- 
nomena. Following  the  Newtonian  assumptions  to  their 
inevitable  conclusion,  we  must  admit  that  the  variation  in  the 
velocity  of  the  satellite  is  due  to  the  rest  of  the  universe  and 
not  to  the  masses  considered.  Newton's  development  of  the 
Keplerian  Laws,  however,  ignores  the  rest  of  the  universe. 
Only  the  grossly  biased  and  obstinate  worshipers  of  mathe- 
matical legerdemain  can  persist  in  the  contention  that  the 


150  SCIENTIFIC  THEISM 

Newtonian  procedure  is  sound  and  justifiable.  The  New- 
tonian implications  force  us  to  admit  interaction.  If  we 
are  to  develop  the  planetary  orbits  consistently  we  must  not 
ignore  the  great  remainder  of  the  universe  for  the  sake  of 
two  comparatively  insignificant  bodies  like  the  sun  and  the 
earth.  Consistent  analysis  therefore  demands  that  we 
attack  the  problems  of  physical  astronomy  by  introducing 
a  two-directional  stress  system  into  the  plane  of  the  orbit. 
A  full  account  of  minor  perturbations  requires  a  three- 
directional  system.  The  plane  of  the  orbit  is  regarded  as 
of  unlimited  extent,  therefore  all  the  activity  factors  within 
this  plane  are  included  in  the  analysis.  For  circular  orbits 
we  consider  the  stress  components  as  being  equal  ifl  magni- 
tude. For  a  two-directional  system  of  unequal  intensities 
the  orbits  will  be  conic  sections  other  than  the  circle.  The 
relative  magnitude  of  the  stress  intensities  controls  the  type 
of  the  orbit.  When  we  proceed  in  this  manner  the  expres- 
sion for  the  orbit  will  involve  the  stress  intensities,  and 
therefore  type  dependence  will  be  directly  related  in  our 
expression  to  these  intensities.  In  other  words,  our  expres- 
sion will  include  a  genuine  physical  activity  relation  capable 
of  accounting  for  the  modifications  of  the  orbits.  We  have 
seen  that  the  mere  inclusion  of  the  velocity  in  the  New- 
tonian expression  constitutes  no  real  physical  reason  for 
these  modifications.  The  ultimate  maintenance  of  the  stress 
intensities  depends  upon  the  Being  of  God.  For  us  science 
is  a  record  of  the  facts  of  the  physical  universe,  ascertained 
experimentally  and  representing,  in  the  final  analysis,  the 
active  thought  of  God. 

96.     Further  Difficulties  of  the  Newtonian  Contention. 

Since  the  time  of  the  battle  royal  between  the  Newton- 
ians and  the  Cartesians,  the  Newtonian  formula  has  reigned 
supreme  in  the  scientific  world.  The  Newtonian  formula, 
possessing  the  quality  of  simplicity  when  contrasted  with 
the  Cartesian  vortex  motion  in  a  frictionless  fluid,  beat 
down  opposition  by  the  sheer  force  of  its  simplicity.  Be 
it  noted,  however,  that  the  Cartesian  development  gives  the 
Keplerian  Laws  as  a  mathematical  consequence^  with  even 
greater  ease  than  the  Newtonian  formula.  We  mention  this 
fact  in  order  to  show  that  the  Newtonian  formula  is  not 


SCIENTIFIC  THEISM  151 

the  only  method  whereby  the  Keplerian  relations  may  be 
developed.  This  misconception  seems  to  be  general  with 
those  who  are  not  familiar  with  the  history  of  physical 
mathematics.  For  this  reason  the  finality  of  the  Newtonian 
position  has  been  accepted  as  practically  self-evident.  Since 
the  pendulum  of  thought  in  the  time  of  Newton  was  swing- 
ing away  from  the  fluid  motion,  the  Newtonian  formula 
gained  the  ascendancy.  The  writer  bears  the  most  profound 
reverence  for  the  great  work  which  Newton  gave  to  the 
world.  Not  very  many  years  ago  he  was  one  of  those  who 
ardently  maintained  that  the  Newtonian  Law  of  Gravitation 
was  the  one  generalization  in  the  history  of  scientific  ad- 
vancement which  would  withstand  the  attack  of  future  gen- 
erations. The  Newtonian  concept  gave  him  such  profound 
satisfaction  that  he  cherished  hopes  that  it  was  an  expres- 
sion which  would  ultimately  explain  all  phenomena  of 
interaction,  including  in  its  domain  the  activities  of  mole- 
cules, atoms,  and  electrons  as  known  to  chemistry,  electro- 
chemistry and  electricity.  The  electrical  law  that  attrac- 
tions and  repulsions  are  commensurate  with  the  product 
of  the  charges  and  inversely  commensurate  with  the  square 
of  the  distance  between  them,  seemed  to  him  to  be  but  a 
further  extension  of  the  Newtonian  generalization  which 
dealt  only  with  attractions.  At  the  seventh  general  meeting 
of  the  American  Electrochemical  Society,  held  at  Boston, 
April  25,  26  and  27,  1905,  he  read  a  paper  entitled  "The 
Interdependence  of  the  Atomic  Weights  and  the  Electro- 
chemical Equivalents"  (Transactions  of  the  American 
Electrochemical  Society) ,  in  which  he  calculated  the  charge 
on  an  electron  from  the  standpoint  of  compressive  work 
done  on  a  spherical  shell.  Not  being  able  to  reconcile  his 
own  view  with  that  of  physics,  which  maintained  that  the 
Newtonian  expression  is  inapplicable  to  molecular,  atomic, 
and  electronic  conditions,  he  endeavored  to  bridge  the  gap 
between  gravitation  and  electricity  before  giving  the  above- 
mentioned  article  its  final  form.  Failing  in  this  attempt  at 
absolute  unification  of  the  two  phenomena  under  the  law 
of  inverse  squares,  he  abandoned  the  solution,  for  the  time 
being,  with  this  statement:  "Gravitational  and  electrical 
mass  may  then  be  regarded  as  the  two  aspects  in  which 
mass  manifests  itself  to  us.  On  the  one  hand  we  have  at- 


152  SCIENTIFIC  THEISM 

tractions,  kinetic  energy,  absorption,  and  integration;  on 
the  other  hand  we  have  repulsions,  potential  energy,  self- 
conservation,  and  differentiation;  yet  these  are  merely  the 
two  modes  in  which  actual  mass  interaction  takes  place/' 

The  reason  for  the  failure  lay  in  his  absolute  confidence 
in  the  Newtonian  law  of  gravitation  which  involves  the 
product  of  the  masses  and  the  inverse  square  of  the  distance. 
If  we  assume  that,  whatever  may  be  the  final  form  of  the 
expression  which  relates  activities  associated  with  mass 
aggregates,  that  same  expression  is  also  capable  of  describ- 
ing the  magnitude  of  the  activities  pertaining  to  the  ulti- 
mate constituent  mass  particles,  we  are  within  the  realm 
of  the  reasonable  and  rational.  If  the  counter-assertion  is 
made  that  the  Newtonian  law  of  inverse  squares  holds  for 
mass  aggregates,  but  does  not  hold  for  the  mass  constitu- 
ents, this  in  itself  is  not  a  sufficient  reason  for  abandoning 
the  above-outlined  postulate,  because  the  law  of  inverse 
squares  may  not  be  a  correct  statement  of  the  magnitude  of 
the  involved  activities.  Consequently  we  propose  to  retain 
this  postulate,  reserving  its  proof  for  a  more  appropriate 
place  in  our  discussion. 

The  remarkable  discrepancy  and  difference  in 
the  behavior  of  electronic  particles  and  mass  ag- 
gregates under  the  Newtonian  formula  is  brought 
startlingly  before  us  when  we  consider  the  fact 
that  the  repulsion  of  two  electrons  is  more  than 
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000 
=  1043  times  greater  than  the  attractive  force  according  to 
the  gravitational  formula.  If  we  consider  the  repulsive 
force  exerted  between  one  gram  of  pure  negative  elec- 
tricity and  another  gram  distant  one  centimeter,  we  ob- 
tain the  enormous  value  of  320,000,000,000,000,000,000,- 
000,000.0=3.2  x  1028  tons.  Moreover,  the  phenomenon  of 
repulsion  itself  is  foreign  to  the  notion  of  gravitation,  which 
deals  only  with  attractions.  Furthermore,  the  startling  dis- 
covery that  the  so-called  mass  of  the  electron  is  not  a  fixed 
quantity,  but  a  variable  magnitude  depending  upon  the  velo- 
city in  such  a  manner  that  the  apparent  mass  increases  with 
an  increase  in  velocity,  places  the  old  notions  of  matter  oper- 
ating according  to  the  gravitational  formula  in  a  precarious 
position. 


SCIENTIFIC  THEISM  153 

We  shall  now  point  out  further  anomalies  in  the  New- 
tonian expression.  In  nature  mass  increase  is  produced  by 
addition — and  not  by  multiplication,  as  in  the  gravitational 
formula — and  the  resultant  associated  activities  are  sums 
and  not  products.  Mechanics,  dealing  with  force  relations, 
finds  thfim  additive  in  their  resultant  effects  and  not  com- 
mensurate with  the  result  obtained  by  multiplication.  In 
this  respect,  therefore,  the  Newtonian  formula  places  itself 
in  flagrant  opposition  to  observed  facts.  Furthermore,  the 
formula  asserts  that  the  force  depends  not  only  upon  the 
product  of  the  masses,  but  upon  an  inverse  ratio  of  the  sec- 
ond power  of  the  distance.  This  latter  assumption  no  doubt 
had  its  origin  in  the  geometric  spatial  analogy  of  a  system  of 
concentric  shells  having  the  center  of  force  emanation  as 
their  common  center.  What  interpretation,  then,  shall  be 
given  to  the  term  "force"?  If  the  emanating  force  is  a 
radiating,  flowing  substance,  then  as  a  definite  quantity 
spreads  itself  uniformly  over  the  surface  of  successive  con- 
centric spherical  shells,  it  is  reasonable  to  suppose  that  the 
quantity  of  the  emanating  fluid  force  per  unit  of  area  will 
stand  in  an  inverse  ratio  to  the  squares  of  the  radii  of  suc- 
cessive shells  because  their  areas  increase  as  the  squares  of 
the  respective  radii.  This  involves  us  at  once  in  a  number  of 
difficulties.  In  the  first  place,  the  motion  of  the  emanating 
fluid  force  must  be  explained.  This  would  necessitate  the 
existence,  at  the  center  of  emanation,  of  an  auxiliary  repel- 
lant  force  capable  of  sending  the  fluid  force  outward  in 
radial  directions.  Secondly,  what  becomes  of  the  diffused 
emanating  fluid  force  if  it  is  not  fortunate  enough  to  become 
attached  to  an  object?  Thirdly,  is  the  supply  of  the  ema- 
nating force,  located  at  the  center  of  emanation,  unlimited 
in  its  available  quantity?  Fourthly,  even  if  all  these  perti- 
nent queries  could  be  answered  satisfactorily,  granting  that 
the  fluid  force  has  arrived  at  its  goal,  an  object,  by  what 
mechanism  can  it  produce  motion  in  the  body?  Fifthly, 
what  is  to  determine  the  direction  of  the  imparted  motion? 

Returning  to  the  conception  of  a  system  of  spherical 
shells,  we  see  that  the  Newtonian  formula  is  analogous  to 
the  case  of  a  fluid  force  dissipating  itself  over  the  surface  of 
a  sphere  and  consequently  experiencing  a  decrease  in  its 


154  SCIENTIFIC  THEISM 

density  proportionate  to  the  inverse  squares  of  the  radii  of 
successive  spheres.  The  intensity  of  the  effect  felt  at  a 
point  on  any  successive  shell  is,  according  to  this  notion, 
directly  proportional  to  the  density  of  the  fluid  force  upon 
the  particular  shell.  No  proof  has  ever  been  produced  to 
substantiate  this  implication  of  the  Newtonian  conception. 
Force  has  never  been  shown  to  be  an  emanating  fluid,  and 
if  this  could  be  proved  it  would  still  be  necessary  to  account 
for  the  fact  that  the  fluid  force  makes  no  distinction  between 
vacuum  and  matter.  It  dissipates  itself  over  the  entire 
spherical  surface  with  mathematical  precision,  irrespective 
of  the  presence  or  absence  of  an  object  in  its  path.  The 
object  receives  that  portion  of  the  force  which  lies  within 
its  own  vectorial  cone,  while  empty  spaces  receive  the  great 
preponderating  remainer.  What  does  empty  space  do  with 
this  remainder?  Many  other  equally  pertinent  questions 
might  be  asked,  but  space  does  not  permit. 

97.  The  Universality  of  the  Inverse  First  Power  Variation. 
Distance  as  an  obstacle  to  the  transmission  of  force,  is 
another  implication  in  the  Newtonian  assumption.  To  the 
writer's  mind  it  seems  more  rational  to  assume  that  distance 
is  merely  a  spatial  symbol  by  which  we  are  informed  in 
regard  to  the  relative  magnitude  of  their  combined  activity 
in  conjunction  with  all  other  active  influences.  In  other 
words,  distance  is  not  an  obstacle  to  action,  but  a  sense 
measure  of  the  inner  relation  of  things  existing  in  an  inter- 
acting unitary  system.  Consequently  we  maintain  that  no 
reason  can  be  found  why  this  inner  relation  or  affinity  must 
be  expressed  as  an  inverse  function  of  the  second  power  of 
the  distance.  If  we  admit — as  we  must — that  distance  is  a 
perceptual  means  of  depicting  the  intensity  of  phenomenal 
relations,  it  does  not  follow  that  the  square  of  the  distance 
is  a  relative  measure  of  the  mutual  effect.  It  is  far  more 
rational  to  suppose  that  the  perceptual  symbol  is  strictly 
proportionate  to  the  relative  effects  made  known  through  it ; 
and  consequently  distance  itself,  expressed  in  its  inverse 
first  power,  must  be  the  ultimate  measure  of  physical  activ- 
ity relationships.  It  may  be  asserted  that  this  is  mere  spec- 
ulation and  that  facts  prove  the  inverse  square  hypothesis. 


SCIENTIFIC  THEISM  155 

We  maintain  that  the  testimony  of  mechanics,  the  testimony 
of  thermodynamics,  and  the  testimony  of  electrochemistry 
bear  out  the  contention  for  the  inverse  first  power  hypothe- 
sis. The  subsequent  portions  of  this  discussion  will  be  de- 
voted to  the  proof  of  this  assertion. 

98.     The  Meagre  Evidence  Serving  as  the  Basis  of  the  New- 
tonian Relation. 

It  is  maintained  that  physical  astronomy  is  impossible 
without  recourse  to  the  Newtonian  formula.  Furthermore, 
it  is  contended  that  this  formula  is  an  absolute  essential  to 
the  science  of  physics.  May  we  inquire,  what  are  these 
facts  that  constitute  the  living  witnesses  which  testify  to 
the  validity  of  the  Newtonian  formula?  In  reply  you  will 
refer  to  the  Newtonian  inference  that  a  central  force  vary- 
ing inversely  as  the  square  of  the  distance  to  the  earth  and 
directly  as  the  product  of  the  sun's  and  earth's  masses  con- 
stitutes a  complete  causal  explanation  of  Kepler's  three 
laws.  The  amount  of  the  moon's  deflection  toward  the  earth 
will  be  cited  as  another  verification  of  the  Newtonian  tenet 
for  the  reason  that  the  amount  of  this  deflection  can  be  cal- 
culated by  the  Newtonian  formula.  The  phenomena  of  the 
tides  will  be  mentioned  as  substantial  evidence.  The  experi- 
ments of  Cavendish,  Cornu,  Wilsing,  Boys,  and  others,  upon 
the  deflection  of  masses  under  the  gravitational  influence 
will  be  used  as  further  corroborative  proofs.  The  fact 
remains,  however,  that  all  these  experiments,  because  of 
their  lack  of  precision,  merely  prove  that  a  type  of  influ- 
ence or  interaction  between  bodies  exists  to  which  science 
has  applied  the  name  gravitation.  Even  hasty  reflection  will 
convince  everyone  of  the  difficulty  of  securing  accurate  data 
concerning  the  phenomena  of  the  tides.  The  same  is  true  of 
the  other  cases  cited.  Therefore  such  cases  do  not  suffice 
to  establish  the  correctness  of  a  formula.  Where  precision 
is  possible,  the  mass-product  relation  of  Newton  cannot  be 
established.  In  such  cases  mass  interactions  are  propor- 
tionate to  the  additive  mass  values  and  not  to  their  products. 
Moreover,  the  spans  between  equilibrated  masses  are  related 
in  accordance  with  the  inverse  linear  function  of  the  first 
and  not  the  second  degree. 


156  SCIENTIFIC  THEISM 

99.  The  Planetary  Orbits  According  to  the  Space-Time  Po- 
tential. 

The  errors  in  the  Newtonian  assumption  have  been 
clearly  pointed  out  in  the  preceding.  If  results  are  obtained, 
in  conformity  with  fact,  from  erroneous  premises,  then  it 
follows  that  the  modtis  operandi  of  obtaining  these  results 
must  also  be  in  error.  In  other  words,  two  compensating 
errors  have  been  introduced  into  the  procedure.  This  bears 
out  our  contention  that  the  Newtonian  formula  itself  is  in 
error. 

The  writer  has  developed  the  Keplerian  relations  from 
premises  which  are  in  complete  accord  with  the  principle 
of  universal  interaction  hereinbefore  set  forth.  Newton 
himself  maintained  the  universality  of  gravitational  inter- 
action, but  abandoned  it  in  his  test  application  to  the  orbital 
motions  of  the  planets.  In  this  way  an  apparent  substanti- 
ation of  his  erroneous  formula  was  secured.  For  the  sake 
of  the  general  reader  we  content  ourselves  here  with  a 
statement  of  the  premises  and  the  significance  of  the  con- 
clusions derived  by  the  mathematical  analysis. 

Our  development  of  the  orbital  equation  is  based  pri- 
marily upon  the  fact  that  space  is  a  sense  chart  of  position 
values  in  such  a  manner  that  the  location  of  a  thing  in 
space  is  determined  by  the  directional  intensity  of  the  inter- 
action at  the  particular  position.  For  purposes  of  analysis 
we  confine  ourselves  to  a  limited  portion  of  this  space.  We 
further  confine  ourselves  to  any  convenient  plane  A  in  space 
whose  extension  we  limit  by  four  lines.  The  plane  A,  thus 
bounded,  is  assumed  to  be  subjected  to  interaction  activity 
intensities  in  accordance  with  our  fundamental  principle. 
In  a  mathematical  analysis  it  is  convenient  to  consider  defi- 
nite components  of  the  activity  intensities.  The  writer  has 
developed  the  following  expression  for  the  path  of  a  body 
free  to  move  in  a  plane  A  subjected  to  the  before-mentioned 
activity  conditions : 

1  J 

x      .     y     _  - 

TI    2  fi   3       ~~    •*"• 


In  this  expression  x  and  y  are  the  coordinates  of  any  point 
in  the  orbital  curve,  and  Fx  and  Fv  are  the  resultant 
activity  intensities.  This  expression  is  the  equation  of  a 


SCIENTIFIC  THEISM  157 

conic  section.  In  the  form  given  it  represents  an  ellipse. 
This  equation  differs  in  a  marked  manner  from  the  New- 
tonian expression  in  that  it  contains  a  genuine  physical 
basis  for  the  types  of  the  orbits.  The  truth  of  this  asser- 
tion is  apparent  from  an  investigation  of  the  expression 
itself,  which  shows  that  the  type  of  the  orbit  depends  upon 
the  relative  magnitude  of  the  activity  factors  Fx  and  Fv 
If  these  factors  are  equal  to  each  other,  the  conic  becomes 
a  circle.  If  they  are  unequal  in  magnitude,  the  curve  is 
an  ellipse  which  tends  toward  a  parabola  when  the  ratio 
of  their  intensities  approaches  an  infinite  value.  Con- 
versely, if  the  orbit  is  an  ellipse,  the  activity  factors  pre- 
vailing in  the  plane  of  the  orbit  are  unequal  in  magnitude. 
For  negative  values  of  '  Fj  the  curve  becomes  an  hyper- 
bola. 

An  exhaustive  investigation  of  a  material  system  inter- 
acting according  to  the  tenets  of  the  Space-Time  Potential 
involves  a  reference  to  a  three-directional  system  of  coordi- 
nate axes.  The  space  of  sense  is  most  conveniently  regarded 
as  a  triply  extended  manifold.  The  Newtonian  relation  is 
derived  from  a  one-directional  vectorial  system  which  re- 
gards the  sun  as  a  central  force.  The  one-directional 
attraction  between  the  sun  and  the  earth  is,  according  to 
Newton,  a  complete  and  sufficient  reason  for  the  earth's 
orbit  type.  We  cannot  agree  with  this  convenient  simpli- 
fication for  the  reason  that  any  finite  portion  of  a  plane  A 
in  space  must  be  under  the  influence  of  a  two-directional 
activity  system.  In  this  manner  only  are  we  able  to  include 
all  the  activity  factors  within  the  plane  beyond  the  confines 
of  the  finite  portion  considered.  By  referring  the  finite  por- 
tion of  the  plane,  as  the  writer  has  done  in  his  development, 
to  an  X  and  Y  axis,  all  activity  factors  in  the  plane  will  be 
either  above  or  below  the  X  axis,  and  to  the  left  or  the  right 
of  the  Y  axis.  In  this  manner  only  can  we  conform  with 
the  requirement  that  the  interaction  be  universal.  New- 
ton's development  fails  utterly  in  conforming  with  this  re- 
quirement, which  is  the  most  important  part  of  his  own 
enunciation. 

The  writer  has  developed  the  Keplerian  relations  by  using 
the  well-known  facts  of  dynamics  without  resorting  to  the 
erroneous  Newtonian  central  mass  attraction  idea  and  the 


158  SCIENTIFIC  THEISM 

inverse  square  hypothesis.  In  these  developments  the 
author  has  adhered  to  the  basic  principle  that  the  body 
which  is  free  to  move  in  the  plane  A  is  actuated  by  the 
activity  factors  Fx  and  Fv. 

These  developments,  in  addition  to  their  intrinsic  inter- 
est, serve  to  demonstrate  the  fact  that  our  basic  thesis  of 
interaction  is  capable  of  constructive  application  resulting 
in  relations  which  conform  with  observed  facts.  In  this 
manner  we  remove  the  possibility  of  substantiating  the 
charge  that  our  work  is  destructive  and  not  construct- 
ive.— See  Appendix  A. 

100.  The  Obliquity  of  the  Ecliptic  Points  to  a  Third  Direc- 

tional Activity  Factor. 

The  inclination  of  the  earth's  axis  to  the  plane  of  its  orbit 
shows  conclusively  that  a  third  activity  factor  influences  the 
system.  Since  the  obliquity  of  the  ecliptic — that  is,  the 
angle  between  the  plane  of  the  ecliptic  and  the  earth's  equa- 
torial plane — is  about  23°  27'  8",  the  angle  which  the  earth's 
axis  makes  with  the  ecliptic  is  about  66°  32'  52".  This  angle 
is  practically  constant  during  the  earth's  elliptical  motion 
in  the  plane  of  the  ecliptic.  Since  the  earth's  semi-diameter 
(according  to  Bessel)  is  20,923,597  feet,  the  distance  h 
along  a  normal  to  the  plane  of  the  ecliptic  from  the  most 
remote  point  of  the  earth's  equatorial  circumference  is 
8,327,260  feet.  During  one  complete  revolution  of  the  earth 
about  its  axis  this  point  traverses  through  a  total  normal 
distance=4ft  in  the  time  23  hours,  56  minutes,  and  4  sec- 
onds=:86,164  seconds.  For  the  distance  h  the  time  is  21,541 
seconds.  This  corresponds  to  an  acceleration  a= 0.035892 

feet  per  second  per  second  along  the  normal  to  the  ecliptic, 

n  i 
since  a—  — .    It  is  therefore  clear  that  the  obliquity  of  the 

ecliptic  cannot  be  maintained  without  the  continuous  activ- 
ity of  a  third  directional  activity  factor. 

101.  Note  on  the  Discrepancy  Between  the  Newtonian  Rela- 
tion and  Dynamics. 

The  Newtonian  relation  states  that  gravitational  attrac- 
tion varies  directly  with  the  product  of  the  masses  m  and 


SCIENTIFIC  THEISM  159 

M,  and  inversely  with  the  square  of  the  distance  s  between 
them ;  that  is,  G  (the  gravitational  attraction)  varies  with 

mM 
8Z  ' 

If  we  employ  the  fundamental  and  experimentally  de- 
monstrable laws  of  motion,  force,  and  work  which  form  the 
very  foundation  of  dynamics,  then  a  radically  different 
expression  results  which  involves  the  sum  of  the  masses 
and  the  distance  to  the  inverse  first  power.  The  truth  of 
the  laws  of  dynamics  has  been  established  by  an  overwhelm- 
ing array  of  experimental  facts.  For  this  and  other  reasons 
already  stated  the  physico-mathematical  developments  of 
the  Space-Time  Potential  are  Non-Newtonian.  See  Ap- 
pendix B. 


CHAPTER  VII 

SOME  APPLICATIONS  OF  THE  SPACE-TIME  POTENTIAL. 

102.     The  Basic  Functions  of  the  Space-Time  Potential. 

We  have  already  shown  that  the  laws  of  motion  of  plane- 
tary bodies  may  be  derived  from  the  principle  of  universal 
interaction  in  a  unitary  system  as  set  forth  in  the  Space- 
Time  Potential.  Without  entering  into  the  details  of  the 
actual  mathematical  analysis,  we  shall  briefly  outline  some 
further  applications  of  the  system. 

We  have  pointed  out  the  fact  that  the  Newtonian  inverse 
square  variation  hypothesis  does  not  agree  with  an  over- 
whelming array  of  easily  ascertained  experimental  facts. 
Dynamics  and  mechanics,  in  toto,  contradict  the  Newtonian 
tenet.  Moreover,  the  Newtonian  hypothesis  fails  utterly  to 
account  for  ultra-atomic  energies.  Whatever  the  laws  may 
be  which  pertain  to  the  ultimate  primordial  particle,  these 
laws  also  hold,  without  modification,  for  the  aggregates  of 
these  particles.  An  increase  or  decrease  in  the  mere  number 
of  these  particles  in  no  way  affects  their  ultimate  nature. 
Sense  perception  tells  a  true  story  of  the  relative  intensity  of 
the  interaction  between  these  particles  and  their  aggregates. 
Therefore  distance  to  the  first  power,  and  not  to  the  second 
power  as  held  by  Newton,  is  the  true  measure  of  the  relativ- 
ity of  the  interaction.  In  ultra-atomic  activities  the  Newton- 
ian relation  must  be  augmented  by  arbitrarily  chosen  con- 
stants in  order  to  account  for  the  developed  intensities. 
Sense  perception  tells  us  that  when  two  particles  are  in  close 
proximity,  the  interaction  is  greater  than  when  they  are  sep- 
arated by  a  greater  distance.  The  direct  testimony  of  sense 
perception  introduces  two  facts:  first,  an  inverse  relation; 
and,  second,  an  actual  distance  which  means  distance  to  the 
first  power.  Newton's  principal  claim  for  the  justification  of 
his  inverse  second  power  relation  is  based  upon  the  alleged 
agreement  with  the  requirements  of  planetary  motion.  The 
errors  involved  in  this  contention  have  been  set  forth.  The 

160 


SCIENTIFIC  THEISM  161 

writer  has  shown  that  the  planetary  relations  can  be  devel- 
oped, without  the  use  of  the  Newtonian  relation,  from  prem- 
ises which  agree  with  fact  and  which  were  held  by  Newton 
himself  only  to  be  abandoned  when  he  attempted  a  direct 
application. 

The  basic  tenet  of  the  Space-Time  Potential  is  that  the 
intensity  of  universal  interaction  varies  inversely  with  the 
first  power  of  the  distance  intervening  between  any  two 
interacting  particles.  By  using  this  principle  a  reconcilia- 
tion, without  the  use  of  arbitrary  constants,  is  effected  be- 
tween celestial  mechanics,  dynamics,  statics,  thermodynam- 
ics, molecular  physics,  electricity,  and  ultra-atomic  activi- 
ties. Our  basic  tenet  may  be  stated  definitely  as  follows: 
the  intensity  of  interaction  Ig  for  any  variable  intervening 
distance  s  between  any  two  activity  factors  A  and  B  varies 
inversely  with  the  distance  s  between  them.  From  this 
statement  is  follows  that 


where  A:  is  a  constant  which  can  be  determined  experiment- 
ally. By  selecting  proper  units  the  constant  k  may  be  made 
equal  to  unity,  and  then  the  expression  is  at  once  recog- 
nized as  the  equation  of  the  hyperbola.  This  relation  con- 
stitutes the  primary  or  hyperbolic  function  of  the  Space- 
Time  Potential. 

By  integrating  this  primary  function  we  obtain  an  ex- 
pression for  the  work  W  done  in  the  displacement  of  an 
activity  factor  from  some  initial  position  to  a  final  position. 
In  order  to  accomplish  this  summation  or  integration  by 
the  calculus  the  so-called  differential  of  the  variable  must 
be  introduced.  In  this  way  we  obtain  the  following 
relation  : 

W 


=  /I8.ds=  /k0)ds  =  k. 


The  latter  expression  constitutes  the  secondary  or  logarith- 
mic function  of  the  Space-Time  Potential. 

Be  it  noted  that  both  of  these  basic  functions  involve 
the  inverse  first  power  of  the  distance.  In  the  following 
paragraphs  we  shall  give  some  of  the  direct  applications  of 
these  functions. 


162  SCIENTIFIC  THEISM 

103.     Some  Typical  Cases  of  the  Primary  or  Hyperbolic  Func- 
tions. 

Boyle's  Law  of  Isothermal  Expansion  of  Gases,  in  which 
the  temperature  remains  constant  during  expansion,  states 
that  the  product  of  the  pressure  p  and  the  volume  v  is  equal 
to  a  constant  c,  that  is, 

pv  =  c  and  p  =  c(  - 


evidently  comes  under  the  primary  or  hyperbolic  function. 
It  is  evident  that  the  volume  is  a  function  of  the  distance  s 
between  the  gas  particles.  For  any  two  given  particles  the 
variation  is  a  function  of  the  inverse  first  power  of  the 
distance  s.  The  resulting  volume  is  due  to  this  type  of  in- 
teractional activity  in  a  three-dimensional  manifold. 

In  the  field  of  electrochemistry  we  find  the  inverse  first 
power  relation  governing  the  activities.  Mass  dissociation 
in  an  electrolytic  cell  due  to  the  action  of  definite  current 
intensities  may  be  representd  by 

M  =  l/- 


where  M  is  the  liberated  mass  in  grams,  r  is  the  current  in 
ampere-hours,  and  h  is  a  constant.  The  above  expression 
may  be  reduced  to  its  primitive  form  : 


(Ma)s  =  F.s  =  C,    and    F- 

In  this  latter  form  it  is  clear  that  electric  dissociation  conies 
under  the  primary  or  hyperbolic  function.  It  is  worthy  of 
note  that,  by  suitable  transformations,  the  distance  factor 
may  be  made  to  appear  as  a  direct  instead  of  an  inverse 
variation.  However,  in  the  former  case  the  expression  will 
be  indicative  primarily  of  something  other  than  a  pure  activ- 
ity intensity. 

The  real  significance  of  the  charge  e  exhibited  by  an 
electron  and  an  ion  is  seen  from  the  expression  — 

mr  =e,  a  constant, 

where  r'  is  the  C.  G.  S.  electrostatic  units  per  unit  of 
valence  necessary  to  liberate  one  gram  of  an  ion,  and  m  is 
the  mass  of  the  ion  using  the  gram  as  the  unit  of  mass. 

From  the  above  expression  it  is  apparent  that  electrical 
relations  are  of  the  same  order  as  the  volume-pressure 


SCIENTIFIC  THEISM  163 

relation  which  pertains  to  gases.  In  other  words,  the 
masses  of  the  ions  are  related  to  the  electrical  intensities 
or  charges  in  the  same  manner  as  the  volume  of  a  gas  is 
related  to  the  applied  pressure.  Herein  we  have  the  real 
meaning  of  the  constancy  of  the  charge  e  which  is  used  so 
frequently  in  modern  electrophysics. 

104.     Essential   Features  of  the   Secondary  or   Logarithmic 
Function. 

According  to  the  Space-Time  Potential,  interaction  is 
unfolded  in  time  upon  that  potential  chart  of  work  values 
which  we  call  space.  Since  space  and  time  are  relativities 
of  the  first  order,  it  follows  that  the  work  values  themselves 
have  only  relative  significance.  The  relative  relations  be- 
tween the  work  values  in  the  most  minute  portion  of  space 
are  deducible  from  the  same  fundamental  function  which 
serves  to  interpret  these  relations  in  a  space  of  unlimited 
extent.  The  writer  has  shown  that  the  secondary  or  loga- 
rithmic function  may  be  used  to  construct  a  space  chart  of 
work  values.  When  this  is  done  we  find  that  this  function 
contains  within  itself  the  story  of  two  worlds:  the  micro- 
cosm, the  small  world  of  positons,  energons,  electrons,  and 
atoms;  and  the  macrocosm,  the  great  world  of  molecules, 
bodies,  and  planets.  When  the  secondary  function, 


=  F(s)  =  (Ma)s  =  /I8.ds= 


is  plotted  from  some  suitable  point  as  a  center,  preferably 
the  point  which  causes  (log£s)  to  equal  zero,  we  obtain  a 
series  of  concentric  loci  which  pertain  to  definite  potential 
work  values.  For  example,  if  we  begin  with  zero  and  take 
any  series  of  n  numbers  like  the  following:  0,  0.01,  0.05, 
0.10,  0.20,  0.30,  0.40,  0.50,  0.60,  0.70,  0.80,  0.90,  1.00, 
1.111/9,  1.25,  1.43,  1.67,  2.00,  2.50,  3.33,  5.00,  10.00,  20.00, 
100.00  .  .  .  etc.  .  .  .  n,  we  find  that  this  group  of 
numbers  divides  itself  into  two  systems  of  positive  and  neg- 
ative work  loci  about  the  number  1.00  as  the  neutral  norm 
of  the  systems.  Suppose,  now,  that  we  adopt  a  convenient 
distance  unit  (centimeter  or  inch)  and  plot  these  values  as 
distances,  beginning  with  zero,  along  the  same  straight  line, 


164  SCIENTIFIC  THEISM 

then  we  have  established  a  condition  which  is  replete  with 
unlimited  physico-mathematical  possibilities.  The  scope 
and  intent  of  this  work  prohibit  a  detailed  exposition  of 
the  writer's  investigations  in  this  field.  We  have  previously 
refuted  materialism  and  we  have  shown  that  a  consistent 
and  true  interpretative  science  must  be  based  upon  philos- 
ophy and  religion,  for  the  reason  that  the  isolation  of  spec- 
ulative science  from  philosophy  and  metaphysics  invariably 
results  in  a  narrow  view  of  the  cosmos  which  therefore  re- 
dounds with  inconsistencies.  In  this  constructive  portion 
of  our  work  we  show  that  consistent  scientific  developments 
possessing  unlimited  unifying  potencies  follow  directly  from 
our  broader  view  of  reality.  We  are  forced  to  confine  our- 
selves to  a  brief  statement  of  some  of  the  particularly  sig- 
nificant developments. 

Returning  to  the  consideration  of  the  n  numbers,  plotted 
as  distances  along  the  same  right  line  from  an  initial  origin 
or  zero  point,  let  us  divide  the  group  of  numbers  into  two 
sub-groups  formed  about  the  point  corresponding  to  the 
number  one,  to  which  the  writer  has  given  the  name  "change 
point"  for  the  obvious  reason  that  the  work  values  change 
their  signs  in  passing  through  this  point.  Beginning  with 
the  change  point  (1),  let  us  designate  all  numbers  greater 
than  1  as  group  G  and  all  values  of  n  less  than  1  as  group 
L.  Group  G  then  is  composed  of  all  values  of  n  from  one 
(1)  to  infinity  ( oo),  and  group  L  is  composed  of  all  values 
of  n  from  one  (1)  to  zero  (0) .  The  author  has  shown  that 
for  all  values  of  n  in  group  G  the  work  value  or  work  con- 
stants are  positive  (-f-),  and  for  all  values  of  n  in  group  L 
the  work  constants  are  negative  ( — ).  Moreover,  he  has 
proved  that  for  any  particular  positive  work  constant 
(-f-W)  calculated  from  a  given  value  of  n  in  group  G,  there 
corresponds  an  equal  negative  work  constant  ( — W)  which 

may  be  calculated  from  the  value  (  -  ) ,  that  is  the  recip- 
rocal of  n  in  the  group  L.  The  work  done  in  displacement 
from  the  change  point  1  to  any  point  n  is  given  by  the 
relation 


SCIENTIFIC  THEISM  165 

Similarly,  the  work  of  displacement  from  point  m  to 
point  n  is  found  from  the  expression 

W  =  k<j  log£  n  -  loge  m  >  =  k  .  log£<  ^  >. 

Moreover,   the   work   done   in   displacement  from  the 
change  point  1  to  any   point      (  -  j       in   group   L   is  ex- 

w 

pressed  by 

W  =  k{log£l  -  loge  QH  =  k  .  loge  M  =  k  .  logen. 

To  illustrate  by  specific  values,  we  find  that  for  a  value  of  n= 
100,  W=+4.605,  and  for  a  valued  -)  =  -!-  =  0.01  we  find  that 
W=-4.605.  Similarly,  for  n  =  1.25,  W=  +0.223,  and  for 
4  =  °'80'  W=  -0.223.  See  Appendix  C. 


If  we  let  S»  be  the  distance  from  the  change  point  1  to 
any  point  n  in  the  group  or  system  G,  and  s*  the  correspond- 
ing distance  from  the  change  point  to  the  point  £  in  the  sys- 
tem L,  then  we  readily  observe  that 

sn  =  (n—  1),  and  Si=-  -  '• 

Thus,  forn  =  2.5,  sn  =  (n-l)  =  (2.5-1.0)  =  1.5,  and 
}         1=0.4,  S<  = 


.,  .. 

2.5  n  2.5 

To  construct  the  two  corresponding  work  loci  we  lay  off  a 
distance  sn=1.5  unit  along  a  straight  line  to  the  right  of  an 
arbitrarily  chosen  change  point,  and  to  the  left  of  the  change 
point  along  the  same  line  we  lay  off  a  distance  s^  =0.60  unit. 

The  value  n  =  2  .  5  corresponds  to  sn  =  1  .  5,    and   for  f  -  J  =  0  .  4, 

54  =  0.60.  The  work  constant  Wn  (corresponding  to  the  value 
n)  —  log  £n  =  log£2  .  5  =  hyperbolic  logarithm  of  2.5  =  +0.916. 
Similarly,  the  work  constant  W&  (corresponding  to  the  value 

-)=loge(-)  =  log£0.  4  =  hyperbolic  logarithm  of  0.4=—  0.916. 
The  corresponding  force  constants  are  : 


166  SCIENTIFIC  THEISM 

Work  or  potential  loci  may  be  plotted  in  any  given  plane 
in  space  concentrically  about  the  change  point  as  a  radial 
center.  Interacting  mass-acceleration  (Af.a)  aggregates 
or  kerns  group  themselves  in  complete  conformity  with  the 
force  loci  of  their  common  plane.  The  particular  spatial 
juxtaposition  of  the  activity  kerns  is  a  direct  consequence 
of  the  innate  character  of  reality  and  not  of  the  coercion  of 
space.  Similarly,  the  ordered  flow  of  change  is  due  to  the 
innate  intent  of  reality  and  not  to  a  coercive  influence  of 
time  regarded  as  an  activity  agent.  In  order  to  clarify 
the  meaning  of  the  above  statements  let  us  consider  the 
two  mass-acceleration  kerns 

Fn  =  Mn.  On  and  F*  =  M*.  a*. 

The  Universal  Law  of  Interaction  exemplified  in  our 
secondary  or  logarithmic  function  is  substantiated  by  all 
known  experimental  facts.  This  law  demands  that  during 
interaction  the  two  kerns  Fn  and  F*  be  continuously 
located  in  the  same  straight  line,  on  opposite  sides  of  their 
common  change  point,  and  in  loci  whose  work  or  potential 
constants  are  equal  in  magnitude  but  opposite  in  sign.  If 
the  two  kerns  be  in  rotation  they  will  continue  to  rotate 
along  loci  of  equal  potential  about  the  change  point  as  a 
common  center  unless  this  form  of  activity  be  modified  by 
the  advent  of  extraneous  influences.  We  give  the  name 
"normal  line"  to  that  straight  line  which  passes  through 
the  change  point  and  upon  which  the  two  kerns  are 
located.  If  the  kern  Fn  is  displaced  away  from  the  change 
point  along  the  normal  line  to  a  locus  of  higher  potential, 
then  the  kern  F&  is  simultaneously  displaced  in  the  opposite 
direction,  to  a  locus  of  the  same  potential  but  opposite  in 
sign.  During  displacement  along  the  normal  line  both  kerns 
undergo  a  change  in  magnitude  which  conforms  with  the 
constants  of  the  traversed  loci.  Herein,  then,  we  find  a 
valid  physical  reason  for  the  Kaufmann  effect.  When  a 
system  is  in  rotation  in  accordance  with  the  mandates  of 
the  universal  law  of  interaction,  we  say  that  it  is  in  a  con- 
dition of  dynamic  equilibrium,  in  contradistinction  to  the 
well  known  terrestrial  condition  of  static  equilibrium.  If 
the  kerns  be  great  aggregates,  as  in  the  case  of  the  sun  and 
the  earth,  then  the  change  point  may  be  found  within  the 


SCIENTIFIC  THEISM  167 

confines  of  the  greater  kern.  The  resulting  orbits  are  loci 
of  equal  potential.  The  type  of  the  orbit  is  a  resultant  of 
the  complexity  of  the  interaction.  It  should  now  be  clear 
that  distance  is  not  a  barrier  to  action,  but  a  measure  of 
its  relativity.  We  may  now  readily  picture  the  relations 
between  the  two  kerns  F»  and  F+.  For  a  value  of  n  —  2.5 
we  must  locate  Fn  =  M»  a*  =  0.6102/3  along  the  normal 
line  at  a  distance  sn  —  1.5  unit.  In  the  oposite  direction 
and  at  a  distance  s+  =  0.60  unit  we  must  locate  the  other 
kern  F£  =  M^  a^  =  1.52  2/3.  If  the  system  be  in  rota- 
tion and  uninfluenced  by  extraneous  factors  (a  purely  theo- 
retical case),  then  the  kerns  will  rotate  about  the  change 
point  in  concentric  circular  orbits  whose  radii  are  desig- 
nated by  the  values  of  sn  and  st  respectively. 

The  product  of  the  kern  magnitude  Fn  by  its  distance  sn 
is  equal  to  the  product  of  F*  by  s*.  This  relation  is  of  the 
same  type  as  that  well-known  relation  in  statistic  which 
pertains  to  the  lever.  A  notable  difference  is  the  fact  that 
the  accelerations  are  different  in  magnitude.  This  is  evi- 
dent if  we  write  the  above  statement  in  terms  of  mass  and 
acceleration  as  follows  ; 


(Mn.an)sn 

The  writer  has  shown  that  the  ratio  between  the  two  ac- 
celerations On  and  a*  is  equal  to  the  value  n  for  all  values 
of  n  greater  than  1.11  £,  and  consequently  for  all  values  of 


-lless  than  0.90.  If  we  make  the  two  accelerations  in  the 

above  expression  equal,  we  can  at  once  deduce  the  law  of 
the  lever,  which  is  the  most  important  principle  in  mechan- 
ics and  statics. 

^ 

Since   n   in   the   above  is  greater  than  1.1  lr,  —  *»n  and 

v  a^ 
o 

a^=— •  The  following  is  self-evident: 

n 

*  *        N 

an\.     ^    ,  =  IM  ad 

n 
therefore  it  follows  that 

(Mn)n.sn  = 

This  expression  is  of  the  same  order  as  the  well-known  law 
of  the  lever.  That  it  is  correct  in  value  as  well  as  form  may 


f  — 


168  SCIENTIFIC  THEISM 

be  shown  by  reducing  it  to  an  identity  by  substituting  the 
following  values : 

Mi=n2(Mn),  and   S-2=n, 

SA 

which  the  writer  has  shown  to  be  true  for  all  values  of  n 
greater  than  1.11  i. 

In  the  terrestrial  gravitation  constant  of  acceleration  g, 
we  find  a  common  case  of  equalized  acceleration  which  modi- 
fies the  general  expression,  as  shown  above,  into  the  form 
expressed  by  the  law  of  the  lever.  For  the  case  of  the  lever 
the  change  point  becomes  the  fulcrum  in  reference  to  which 
the  arm  of  M&  is  s*  and  the  arm  of  Mn  is  nsn.  The  fol- 
lowing is  noteworthy : 

Mi     n.sn 
__  = =na. 

Mn         Si 

By  this  relation  in  the  well-known  law  of  the  lever  is  linked 
to  the  "genital  number"  n  of  the  Space-Time  Potential. 

A  simple  numerical  example  will  serve  to  illustrate  the 
relation  between  dynamic  and  static  equilibrium  outlined 
above. 

Let  the  genital  number  n  =  2.5,  as  above.  For  this  value 
of  n  the  work  constants  are  -f  Wn  =  -f-  0.916  and  —  W* 
=  —  0.916.  The  corresponding  force  constants  are 
F,  =  -}-  0.610%  and  F*  =  —  1.1 


CASE  I.   DYNAMIC  EQUILIBRIUM 

The  mass  M»  =  unity  is  located  on  the  work  locus  -f  PF« 
at  a  distance  s«  =  1.5  unit  from  the  change  point. 

The  mass  M*  —  n2  (Mn)  =  (2.5) 2  (1.0)  =  6.25  units  is 
located  on  the  work  locus  —  W&  at  a  distance  Si  =  0.60 
unit  from,  but  on  the  other  side  of,  the  change  point,  all 
three  points  being  on  the  normal  line.  The  following  re- 
lation holds : 

F«.  s«  =  Fi.  SA  and  +   0.610%    (1.5)    =   1.52%    (—0.6) 
=W«  =  0.916. 

CASE  II.    STATIC  EQUILIBRIUM 
This  is  the  case  of  the  ordinary  lever. 

The  mass  Mn  =  unity  is  located  at  a  distance  n(sn)  — 


SCIENTIFIC  THEISM  169 

2.5  (1.5)  =  3.75  units  from  the  change  point,  which  now 
constitutes  the  fulcrum  of  the  lever.  The  Mass  M*  =  6.25 
units,  as  previously,  remains  located  as  in  Case  I.  Then  we 
have  the  following  : 


and  (1.0)   (2.5)   (1.5)  =  (6.25)   (0.60)  =  3.75. 

It  is  evident  that  for  Af»  =  unity  the  constant  for  this 
system  is  n  (sfl). 

Although  the  scope  of  the  main  portion  of  this  work  pro- 
hibits a  mathematical  treatment,  nevertheless  it  would  be 
unfortunate  to  omit  the  simple  relations  which  unfold  them- 
selves as  a  consequence  of  the  philosophical  contemplation  of 
the  physical  universe. 

105.     Macrocosmic  Relations. 
Let 

n  =  the  genital  number, 

Wn  =  the  work  done  from  the  change  point  1  to  the 

point  n, 
Wt  =  the  work  done  from  the  change  point  1  to 

the  point  (4)    (this  work  is  the  same,  irrespec- 

tive of  direction), 

tn  =  time  of  translation  through  distance  s«, 
t&  =  time  of  translation  through  distance  34, 

then,  for  values  of  n  greater  than  1.11$  and  for  (A)  less 
than  0.90,  the  following  relations,  derived  from  the  second- 
ary or  logarithmic  function,  hold  good  : 

Wff  —  WA  =  the  hyperbolic  logarithm  of  the  genital 
number  n; 


a*     Mn.a 


These  relations  pertain  to  celestial  mechanics  and  mole- 
cular physics.  In  conjunction  with  the  ordinary  laws  of 
motion,  and  by  suitable  modifications  to  conform  with  ter- 


170  SCIENTIFIC  THEISM 

restrial  conditions,  these  relations  constitute  the  funda- 
mentals of  macrocosmic  mechanics.  The  resulting  values 
receive  their  proper  interpretation  through  the  selection 
of  suitable  units. 

106. — Microcosmic  Relations 

By  means  of  the  secondary  or  logarithmic  function  we 
may  pass  with  precision  from  the  macrocosm  to  the  micro- 
cosm without  resorting  to  constants,  arbitrarily  chosen,  in 
order  to  reconcile  the  glaring  discrepancies  which  arise  in 
the  old  physics.  For  values  of  n  less  than  1.111%  and  of 
(A)  greater  than  0.90,  the  following  relations,  derived 
directly  from  the  secondary  or  logarithmic  functions, 
obtain : 
Wn=Wj;  th=t2;sn=8i;  vn=v^;  an=aji;  Mn=M_i;  Mn.aB=Mi.ai. 

n  n  •  n  n  n  n       a 

Our  secondary  function  takes  us,  without  apology,  into 
the  world  of  atoms,  positons,  energons,  and  electrons.  It 
is  noteworthy  that  the  orbital  radii  in  the  microcosm  are 
equal  for  a  given  system  derived  from  a  particular  genital 
number.  We  have  seen  that  in  the  macrocosm  they  are 
unequal  and  that  their  ratio  is  expressed  by  n,  the  genital 
number. 

107.     Applications  of  These  Relations. 

Using  the  expression  pertaining  to  motion  in  conjunction 
with  the  relations  previously  set  forth,  the  writer  has  cal- 
culated the  charge  e  exhibited  by  an  electron.  In  these  cal- 
culations the  mass  of  the  electron  was  assumed  to  be  that 
which  corresponds  to  a  velocity  v  =  3.0  X  109  centimeters 
per  second  =  ^  of  the  velocity  of  the  light  in  air.  For 
this  velocity  the  mass  of  the  electron  is  practically  constant. 
The  writer's  calculated  value  of  e  =  4.77  X  10~10  C.  G.  S. 
electrostatic  unit  corresponds  closely  with  the  experimental 
values  derived  by  H.  A.  Wilson  (e  —  3.1  X  10-10.),  J.  J. 
Thomson  (e  —  3.4  -f  10-10)  and  R.  A.  Millikan  (4.77  X 
10-10) .  See  Appendices  B  and  D. 

An  important  fact  was  disclosed  by  these  calculations. 
It  became  evident  that  the  masses  of  ions  and  electrons  are 
related  to  the  electrical  intensities  in  the  same  way  that  the 
volume  of  a  gas  is  related  to  the  applied  pressure.  This  fact 


SCIENTIFIC  THEISM  171 

constitutes  another  confirmation  of  the  fundamental  tenets 
of  the  Space-Time  Potential. 

The  writer  has  employed  the  above  fundamental  rela- 
tions in  the  calculation  of  the  physical  dimension  of  mole- 
cules. The  method  is  free  from  the  mathematical  com- 
plexity of  the  prevalent  methods.  The  writer's  method  con- 
sists briefly  in  the  determination  of  the  genital  number  n 
which  corresponds  to  the  decomposition  voltage  for  any 
particular  molecule.  Thus  in  the  case  of  the  hydrochloric 
acid  molecule,  whose  normal  solution  has  a  decomposition 
voltage  of  1.31  volts  =  0.0043666  C.  G.  S.  electrostatic  unit 
of  potential  difference,  we  find  that  the  work  constants  equal 
1.99322  X  10-19.  The  distance  s»  from  the  change  point  to 
the  center  of  the  hydrogen  atom  is  found  to  be  2.47730  X 
10— '  cm.  Similarly,  the  distance  34  from  the  change  point 
to  the  center  of  the  chlorine  atom  is  found  to  be  0.41755  X 
10— 8  cm.  The  distance  center  to  center  of  the  hydrogen  and 
chlorine  atoms  is,  then,  the  sum  of  these  values;  that  is, 
2.89485  X  10—*  centimeters.  This  result  is  in  complete  con- 
formity with  results  derived  by  totally  different  and  far  less 
direct  methods  of  investigation. 

108.    Theory  of  Relativity. 

Were  we  asked  to  choose  the  most  stupendous  of  the  un- 
limited number  of  marvels  and  mysteries  extant  in  the  phy- 
sical universe,  we  feel  certain  that  no  error  would  be  com- 
mitted if  we  selected  the  phenomenon  of  light.  How  a  per- 
son of  sound  mind  can  remain  a  materialist  after  contem- 
plating the  infinite  profundities  involved  in  the  phenomenon 
of  light  is  beyond  comprehension.  That  the  world  is  far 
more  than  matter  and  chance  should  be  evident  to  any  per- 
son free  from  bias,  after  nothing  more  than  a  hasty  survey 
of  this  most  marvelous  phenomenon.  Not  least  of  its  many 
marvels  is  the  extraordinary  fact  that  the  velocity  of  light 
(3  X  1010  centimeters  per  second)  is  a  constant,  irrespec- 
tive of  the  velocity  of  the  observer.  If  an  observer  travelled 
in  an  aeroplane,  in  the  direction  of  the  propagation  of  light, 
at  the  velocity  of  100  miles  per  hour,  then  if  it  were  possible 
to  increase  this  velocity  to  100,000  miles  per  hour  the  ob- 
served velocity  of  propagation  of  light  would  still  remain 
the  same.  The  broad  interpretation  of  the  experiments  of 


172  SCIENTIFIC  THEISM 

Michelson  and  others  leads  to  this  astounding  conclusion. 
This  fact  forms  the  basic  nucleus  of  the  modern  theory  of 
relativity.  H.  A.  Lorentz  has  attempted,  with  exceptional 
ingenuity,  to  derive  a  physical  basis  for  the  theory  of 
relativity.  Lorentz  believes  that  an  independent  ether  inter- 
acting in  a  compressional  manner  with  electronic  matter 
provides  the  desired  physical  basis  for  the  principle  of 
relativity.  Poincare  has  done  much  to  further  this  view. 
We  are  at  one  with  these  investigators  in  their  contention 
that  the  root  of  relativity  is  found  in  interaction,  but  we 
differ  with  them  in  their  conclusion  that  the  interaction 
factors  are  radically  different  in  their  ultimate  nature.  We 
find  our  physical  justification  for  the  principle  of  relativity 
in  the  interaction  between  the  concurrent  and  excitant 
masses  in  accordance  with  the  relations  inherent  in  our 
primary  and  secondary  functions.  According  to  our  view, 
the  excitant  mass  (of  sub-atomic  magnitude),  during  its 
translatory  progress  through  the  concurrent  system,  com- 
posed of  gyratory  groups  of  energons,  interacts  therewith  in 
a  manner  productive  of  those  vibratory  oscillations  known 
generally  as  waves  of  light.  Electric  oscillations  are  of  the 
same  general  order  and  are  produced  in  a  similar  manner. 
For  the  phenomena  of  light  and  genital  number  n  =  v,  the 
velocity  of  light  (3  x  1010  centimeters  per  second). 
Letting  the  subscript  n  refer  to  the  excitant  system  and  the 
subscript  (4)  to  the  concurrent  system  and  using  the 
macrocosmic  relations  (paragraph  105),  we  have  the  fol- 
lowing expressions  on  the  basis  of  a  unit  of  time : 

BB  =  vn=  (n— 1)  =  (V— 1),    for  the  excitant  system,  and 
34  =  V4  =  - — — •«- — y — ,     for  the  concurrent  system. 
From  this  it  follows  that: 

^  =  V;    (vn+v*)  =(Bn+Bft)=ff!z±)=  practically    V. 

This  means  that  the  ratio  of  the  velocity  vn  of  the  excitant 
system  to  the  velocity  V&  of  the  concurrent  system  is  always 
equal  to  the  constant  velocity  V  of  light.  Moreover,  the 
total  energized  space,  for  a  period  of  interaction  equal  to 
one  second,  is  practically  equal  to  the  same  constant  V.  The 
constancy  of  the  velocity  of  light  arises  out  of  the  relative 


SCIENTIFIC  THEISM  173 

velocities  of  the  excitant  and  the  concurrent  systems.  In 
this  fact  we  have  a  genuine  physical  basis  for  the  principle 
of  relativity.  The  present  extent  of  our  knowlege  of  physi- 
cal facts  indicates  that  the  maximum  value  of  the  genital 
number  n  which  obtains  in  the  physical  universe  is 
n  =  V  =  3  X  1010.  That  the  velocity  vn  of  the  electronic  ex- 
citant system  can  never  equal  the  value  V  is  evident  from 
the  expression  vn  —  (n  —  1)  =  (V  —  1).  The  velocity  v& 
of  the  concurrent  system  differs  inappreciably  from  one 
centimeter  per  second  or  a  little  less  than  two  feet  per 
minute.  The  effect  of  so  slight  a  translatory  motion,  is 
negligible  as  far  as  terrestrial  conditions  are  concerned. 
The  distance  K  traversed  by  light  in  one  second  is  the  cos- 
mic unit  of  distance.  The  writer  has  given  the  name  "Kos- 
mometer"  to  the  distance  K  =  3  X  1010  centimeters.  The 
Kaufmann  effect  finds  its  interpretation  in  the  secondary 
function  by  making  the  unit  distance  from  the  change  point 
to  the  origin  of  coordinates  equal  to  st  =  y%K.  Velocities  v 
plotted  from  the  change  point  along  the  horizontal  or  X  axis 
will  then  appear  as  fractions  of  the  velocity  V  for  the  time 
unit  one  second.  The  work  constant  for  any  velocity  v  is 
then  the  vertical  ordinate  corresponding  to  the  value 
(v  -r-  V)  measured  from  the  change  point.  By  applying  the 
fundamental  relations  of  the  secondary  function  to  this 
system  the  writer  has  developed  the  following  expression 
for  the  force  (mass-acceleration)  kern 


F 


That  the  variation  of  the  velocity  v  has  practically  no  effect 
upon  the  value  of  F&  up  to  a  value  of  v  —  0.01  V  is  brought 
out  by  applying  the  above  expression  to  values  of  v  ranging 
from  zero  to  0.01  V.  On  a  unit  basis  the  total  increase  in 
F£  over  this  wide  range  is  only  0.005.  If  we  take  the  value 
of  F£,  which  corresponds  to  v  •=.  0.01  V,  as  a  base,  then  the 
ratios  of  FA  to  this  base,  for  values  of  v  increasing  from 
v  —  0.01  V  to  v  =  V,  are  in  conformity  with  the  experimen- 
tal results  established  by  Kaufmann.  In  fact,  the  average 
conformity  is  greater  than  the  average  agreement  arising 


174  SCIENTIFIC  THEISM 

fiom  the  use  of  the  following  expression  by  Lorentz  and 
Einstein : 

m  _  1 

mn 


For  Lorentz  this  expression  indicates  a  contraction  of 
the  electrons  during  translatory  motion  due  to  the  pressure 
of  the  ether.  Referring  to  this  theory  of  Lorentz,  H.  Poin- 
care  states  in  his  work  "Science  and  Hypothesis" :  "It  is  in 
contradiction  to  Newton's  law  that  action  and  reaction  are 
equal  and  opposite — or,  rather,  this  principle,  according  to 
Lorentz,  cannot  be  applicable  to  matter  alone ;  if  it  be  true, 
it  must  take  into  account  the  action  of  the  ether  on  matter, 
and  the  reaction  of  the  matter  on  the  ether."  * 

The  writer's  expression,  derived  from  the  basic  relations 
of  the  Space-Time  Potential,  affords  a  complete  justification 
in  the  generalized  conception  of  action  and  reaction  involved 
in  the  principle  of  interaction  between  two  material  sys- 
tems, the  excitant  and  the  concurrent  systems;  that  is,  be- 
tween secondary  and  primary  matter.  Our  expression  con- 
forms with  the  requirements  of  the  Kaufmann  effect,  which 
shows  that  for  a  velocity  increase  beyond  a  certain  crucial 
velocity  the  kern  magnitude  increases  toward  an  infinite 
limit  as  the  velocity  of  light  V  is  approached.  The  inability 
of  the  electron  to  reach  an  infinite  magnitude  indicates  that 
this  kern  can  never  acquire  the  velocity  of  light.  The  above 
facts  involve  the  complete  relativity  of  energy,  force,  mass, 
space,  and  time.  See  Appendix  E. 

109.    The  Structure  of  the  Atom. 

J.  J.  Thomson  battled  bravely  and  with  profound  mathe- 
matical sagacity  to  produce  a  stable  mechanistic  atom  from 
an  electronic  protostructure.  Thomson's  atom  consists  of  a 
positively  charged  (whatever  that  is)  outer  sphere  having 
electrons  disposed  uniformly  upon  one  or  more  inner  con- 
centric spheres.  Rutherford,  finding  the  Thomsonian  atom 
incapable  of  explaining  the  numerous  phenomena  of  radio- 

1  Science  and  Hypothesis,  p.  175. 


SCIENTIFIC  THEISM  175 

activity,  adopted  the  Saturnian  type  of  atom  suggested  by 
Nagaoka  in  1904.  Nagaoka's  atom  is  practically  the  Thom- 
sonian  atom  turned,  as  it  were,  inside  out.  A  large  positive 
nucleus  is  placed  arbitrarily  at  the  center,  while  the  elec- 
trons are  arranged  upon  a  series  of  concentric  exterior 
shells.  Both  types  of  atoms  are  expressions  of  a  desire 
mechanistically  to  combine  and  unify  the  two  phases,  the 
positive  and  the  negative,  inherent  in  all  phenomenal  ac- 
tivity, without  a  sufficient  ground  in  the  nature  of  reality 
for  the  manner  of  their  unification.  In  the  very  nature  of 
things,  these  two  phases  have  never  been  separated,  there- 
fore their  unification  is  unnecessary.  The  Space-Time  Po- 
tential shows  us  the  nature  of  their  eternal  union,  and  we 
are  not  called  upon  to  combine,  in  an  arbitrary  way,  that 
which  is  already  unified  in  a  definite,  unchanging  manner. 
According  to  the  Space-Time  Potential,  an  atom  is  composed 
of  neutral  energons,  capable  of  positive  and  negative  inter- 
action in  conformity  with  the  dictates  of  prevailing  condi- 
tions, and  arranged  along  concentric  work  loci  whose  com- 
mon center  constitutes  the  change  point  of  the  system. 
Every  work  locus  has  its  positive  and  its  negative  phase. 
A  positive  work  factor,  with  its  inseparable  yet  equal  nega- 
tive antipodal,  constitutes  a  unitary  activity  factor  capable 
of  two-directional  activity  (positive  and  negative)  proceed- 
ing from  a  primary  neutral  condition.  Matter  is  therefore 
capable  of  exhibiting  three  phases  of  activity — the  neutral 
or  primary  phase  and  the  positive  and  negative  phases, 
known  herein  as  secondary  matter. 

The  molecule  of  the  Space-Time  Potential  consists  of 
atomic  groups  arranged  along  the  work  loci  about  a  result- 
ant change  point  in  conformity  with  the  requirements  of 
the  secondary  function.  In  molecular  systems  we  have  seen 
that  the  radial  magnitude,  measured  from  the  resultant 
change  point  to  the  atomic  centers  located  upon  work  loci 
of  equal  potentials,  are  unequal. 

110.     Metageometry  and  Space. 

The  first  hints  of  a  metageometry  or  non-Euclidean 
geometry  are  found  in  the  work  of  Nasir  Eddin  (1201- 
1274).  Girolamo  Saccheri  (1667-1733),  a  learned  Jesuit, 
studied  the  problem  of  parallels  from  a  new  viewpoint. 


176  SCIENTIFIC  THEISM 

Another  point  of  attack  was  secured  by  Johann  Heinrich 
Lambert  (1728-1777).  The  interest  taken  in  this  subject 
is  evident  when  we  mention  the  following  renowned  con- 
tributors to  its  theories:  Gauss,  Riemann,  Lobatchevsky, 
Janos  Bolyai,  Helmholtz,  Grassmann,  Cayley,  Felix  Klein, 
Simon  Newcomb,  Paul  Stackel,  Friedrich  Engel,  G.  B.  Hal- 
sted,  H.  Poincare,  B.  J.  Delboeuf,  Ernst  Mach,  Bertrand  A. 
W.  Russell,  Beltrami,  and  Sophus  Lie. 

Pangeometry  or  metageometry  is  essentially  non-Eu- 
clidean. These  speculations  grew  out  of  the  consideration 
of  that  axiom  of  Euclid  which  states  that  but  one  straight 
line  can  be  drawn  through  a  given  point  parallel  to  a  given 
straight  line.  According  to  Euclidean  geometry,  two 
straight  lines  are  parallel  when  they  lie  in  the  same  plane 
and  cannot  meet  or  approach  each  other,  however  far  they 
may  be  produced.  Moreover,  since  parallel  lines  cannot 
approach  each  other,  they  are  everywhere  equally  distant 
from  each  other.  Lobatchevsky  and  Bolyai  claim  that  it 
is  impossible  to  prove  that  only  one  straight  line  can  be 
drawn  through  a  given  point  parallel  to  a  given  straight 
line.  Because  of  this  alleged  inability  to  prove  this  Euclid- 
ean axiom,  Lobatchevsky  assumed  that  several  parallels  may 
be  drawn  through  a  given  point  to  any  given  straight  line. 
Both  Lobatchevsky  and  Bolyai  believed  that  this  assump- 
tion constituted  a  generalization  which  made  of  Euclidean 
geometry  a  particular  and  limited  branch  of  an  all-inclusive 
pangeometry.  For  Lobatchevsky  the  sum  of  the  angles  of  a 
triangle  is  always  less  than  180°,  and  the  difference  between 
their  sum  and  180°  is  proportional  to  the  area  of  the  tri- 
angle. Furthermore,  Lobatchevsky  holds  that  a  figure  simi- 
lar to  a  given  figure  but  of  different  dimensions  cannot  be 
constructed.  Pangeometry  includes  the  following  three 
distinct  positions : 

I.    Euclid. 

1.  Only  one  straight  line  can  be  drawn  through  a  given 
point  parallel  to  a  given  straight  line. 

2.  The  sum  of  the  three  angles  of  any  triangle  is  equal 
to  180°. 

3.  Space  regarded  as  infinite.     The  perspective  view  of 
infinitely  distant  parts  of  a  plane  is  a  straight  line. 


SCIENTIFIC  THEISM  177 

II.  Lobatchevsky. 

1.  From  a  given  point  outside  of  a  given  straight  line 
two  classes  of  lines  may  be  drawn — cutting  and  not  cutting. 
The  not  cutting  lines  constitute  the  parallel  lines  for  Lobat- 
chevsky, and  of  these  there  can  be  an  infinite  number. 

2.  The  sum  of  the  three  angles  of  any  triangle  is  less 
than  180°  by  an  amount  which  is  proportional  to  the  area 
of  the  given  triangle. 

3.  Space  regarded  as  both  immeasurable  and  limited.  The 
perspective  view  of  infinitely  distant  parts  of  a  plane  is  a 
circle. 

4.     The  straight  line  is  the  limit  of  curvature  for  a 
sphere  of  infinite  radius  and  zero  curvature. 

5.  Lobatchevsky's  geometry  deals  with  surfaces  of  con- 
stant negative  curvature.  These  are  the  pseudo-spherical 
surfaces. 

III.  Riemann. 

1.  No  line  can  be  drawn  through  a  given  parallel  to  a 
given  line  in  the  space  of  Riemann. 

2.  The  sum  of  the  three  angles  of  any  triangle  exceeds 
180°  by  an  amount  which  is  proportional  to  the  area  of  the 
given  triangle. 

3.  The  space  of  Riemann  is  unbounded  but  finite. 

4.  Riemann's  geometry  deals  with  surfaces  of  constant 
positive  curvature.    The  infinitesimal  dwellers  in  the  spheri- 
cal surface  of  Riemann  may  move  forward  forever,  and  yet 
their  world  is  finite.    Such  beings  by  looking  forward  can 
see  their  own  backs. 

The  extension  of  these  and  similar  mathematical  specu- 
lations has  led  to  the  notion  of  a  space-family  consisting 
of  an  endless  variety  of  spaces.  Tridimensional  space  is 
merely  one  type.  The  pangeometers  insist  that  we  must 
broaden  our  notion  of  space  to  include  such  types  as  space 
of  four,  five,  and  n  dimensions.  These  flights  of  fancy 
should  permit  the  existence  of  an  appropriate  order  of  be- 
ings corresponding  to  the  various  types  of  space.  A  four- 
dimensional  being,  according  to  this  view,  is  as  far  superior 
to  a  three-dimensional  creature  as  the  three-dimensional 
being  surpasses  the  two-dimensional  animal.  A  two-dimen- 
sional being  cannot  remove  itself  from  the  surface  which 


178  SCIENTIFIC  THEISM 

constitutes  its  world  of  possible  motion.  The  three-dimen- 
sional being  can  move  along  three  distinct  directions.  Con- 
sequently, the  three-dimensional  being  can  easily  remove  the 
two-dimensional  being  from  its  surface  world  without  cross- 
ing a  single  line  within  this  surface.  Similarly,  the  four- 
dimensional  being  can  remove  a  three-dimensional  being 
from  the  interior  of  a  closed  box  without  breaking  through 
any  of  the  enclosing  walls.  Whatever  assurance  we  have 
that  we  shall  not  be  suddenly  removed  from  this  sordid 
world  of  three  dimensions  without  leaving  the  slightest 
trace  must  be  grounded  in  an  absolute  faith  that  the  four- 
dimensional  beings  are  entirely  free  from  thievish  ten- 
dencies. 

A  cursory  inspection  of  the  speculations  of  the  non-Eu- 
clideans  shows  startling  quirks  and  curious  quips  in  the 
mental  processes  of  the  modern  mathematicians.  There  can 
be  no  real  objection  to  Lobatchevsky's  division  of  lines  into 
two  classes — the  cutting  and  the  non-cutting — provided  that 
he  refrains  from  making  the  word  "parallel"  synonymous 
with  "not  cutting/'  If  we  hold — as  we  must — that  a 
straight  line  can  be  extended  indefinitely  without  limit  in 
its  own  direction,  then  only  one  "not  cutting"  line  can  be 
drawn  through  a  given  point  outside  of  a  given  line.  This 
one  "not  cutting"  line  will  then  constitute  the  parallel  line 
of  Euclidean  geometry.  If  we  arbitrarily  limit  the  lengths 
of  straight  lines,  then  we  can  draw  a  number  of  "not  cut- 
ting" lines,  but  how  shall  we  determine  the  magnitude  of 
the  imposed  limit?  If  we  retain  the  definition  of  parallel 
lines  which  states  that  straight  lines  are  parallel  when  they 
lie  in  the  same  plane  and  cannot  meet  nor  approach  each 
other,  however  far  they  may  be  produced,  then  it  is  folly  to 
speak  of  an  infinite  number  of  parallel  "not  cutting"  lines. 
Lobatchevsky  entangles  himself  in  a  species  of  Kantian 
antimony  in  his  speculations  concerning  the  finite  and  the 
infinite.  By  placing  unwarranted  restrictions  upon  our 
a  'priori  space  construction  he  builds  up  a  mathematical 
system  of  space  relations  which  are  mentally  and  logically 
consistent  within  the  imposed  unwarranted  restrictions. 
This  criticism  holds,  with  equal  force,  for  the  system  of 
Riemann  and  all  the  other  pangeometers.  All  the  meta- 
geometers  fail  to  realize  that  space  is  both  a  priori  and  a 


SCIENTIFIC  THEISM  179 

posteriori,  that  it  has  both  subjective  and  objective  signifi- 
cance. Were  this  not  true,  any  person  could  construct  for 
himself  ideal  spaces  whose  number  would  be  limited  only 
by  the  fertility  of  his  imagination.  We  must  draw  a  sharp 
distinction  between  real  space  and  mathematical  space. 
Speculations  concerning  mathematical  spaces  may  be  both 
amusing  and  profitable  to  the  mathematician,  but  these  men- 
tal products  must  be  clearly  differentiated  and  labeled  as 
"speculative  products"  and  not  realities.  Real  objective 
space  is  tridimensional  and  all  the  speculative  a  priori  spaces 
of  the  pangeometers  are  nothing  more  than  mental  by- 
products of  objective  space.  It  is  impossible  crudely  to 
represent  or  interpret  these  a  priori  spaces  without  resort- 
ing to  the  relations  which  pertain  to  real  space.  It  may  be 
interesting  to  speculate  concerning  the  antics  of  a  two- 
dimensional  being  of  zero  thickness  in  a  spherical  surface, 
but  common  sense  prohibits  us  from  assigning  genuine  phy- 
sical reality  to  such  thought  creations.  We  may  be  men- 
tally pleased  with  the  strict  code  of  honor  observed  by  the 
imaginary  beings  which  inhabit  an  imaginary  four-dimen- 
sional space,  but  to  attribute  reality  to  these  creatures  of 
imagination  is  folly.  Every  theorem  of  pangeometry  can 
be  restated  in  terms  of  Euclidean  geometry.  From  ordinary 
Euclidean  geometry  we  know  that  the  sum  of  the  angles  of 
a  spherical  triangle  is  greater  than  two  and  less  than  six 
right  angles.  Riemann's  geometry,  therefore,  is  little  more 
than  a  new  version  of  spherical  Euclidean  geometry.  It  has 
been  claimed  for  pangeometry  that  it  is  a  broader  concept 
than  the  Euclidean.  There  is  little  justice  in  this  conten- 
tion. Every  form  of  pangeometry  arises  out  of  a  limita- 
tion placed  upon  the  concepts  of  Euclidean  geometry.  We 
cannot  hope  to  broaden  the  "a  priority"  of  our  space  notions 
by  mental  effort.  The  subjective  spatial  endowment  of  a 
normal  human  being  stands  in  a  constant  relation  to  the 
objective  world.  Tridimensional  space  arises  invariably  as 
the  result  of  interaction  between  the  subjective  and  the 
objective  world.  No  amount  of  mental  effort  will  "broaden" 
this  into  a  four-dimensional  interactional  resultant.  There- 
fore we  insist  that  every  type  of  pangeometry  is  a  particu- 
larization  and  limitation  of  tridimensional  or  Euclidean 
geometry.  Moreover,  our  subjective  endowment  guaran- 


180  SCIENTIFIC  THEISM 

tees  the  "a  priority"  of  geometry  and  mathematics.  It  fol- 
lows that  the  reality  of  speculative  or  mathematical  spaces 
can  be  determined  only  through  the  experience  of  interac- 
tion with  the  objective  world.  Mathematical  spaces  which 
do  not  conform  with  this  requirement  of  experience  must 
be  regarded  merely  as  products  of  mathematical  imagina- 
tion. Real  space  guarantees  the  possibility  of  actual  motion 
in  every  conceivable  direction.  Mathematical  space  is  a 
mental  product  which  involves  laws  of  imaginary  motion. 
When  mathematical  space  is  tridimensional,  then  the  laws 
of  imaginary  motion  agree  with  those  of  real  motion. 
Bodies  in  space  are  limited  and  finite  in  magnitude.  Things 
are  related.  Space  is  one  type  of  relation  existing  between 
things.  Relations  admit  of  continuity,  while  things  are  dis- 
crete. Herein  we  find  the  norm  of  the  significance  of  the 
infinite  and  the  finite.  Space  being  a  relation,  it  permits  of 
an  infinite  progression.  Therefore  we  are  correct  in  postu- 
lating infinity  of  space.  Geometry  is  not  an  experimental 
science.  There  is  no  absolute  straight  line  in  nature.  The 
nearest  approach  to  a  straight  line  in  nature  is  the  apparent 
boundary  line  between  sky  and  sea,  and  we  know  that  this 
boundary  is  not  a  straight  line.  Geometry  is  an  a  priori 
science  arising  out  of  our  subjective  endowment.  No 
astronomical  triangle  will  prove  or  disprove  the  a  priori 
truth  that  the  sum  of  the  angles  of  any  plane  triangle  is 
equal  to  two  right  angles.  From  the  above  brief  discussion 
it  is  evident  that  the  pangeometers  have  fallen  into  the  same 
error  that  is  so  common  with  the  modern  physicist ;  that  is, 
attributing  reality  to  mere  mathematical  speculation.  The 
facts  of  experience  constitute  the  only  true  touchstone  of 
reality.  Using  this  criterion  on  the  work  of  the  pange- 
ometers, we  find  it  of  speculative  interest  and  value  as  a 
study  in  mathematical  manipulation.  As  a  contribution  to 
our  knowledge  of  space,  the  work  of  the  non-Euclideans  is 
of  little,  if  any,  value,  for  the  reason  that  we  cannot  even 
think  except  in  tridimensional  terms. 

111.     Poincare  on  Central  Forces. 

After  this  work  was  completed  the  writer  ran  across  the 
splendid  work  of  H.  Poincare  entitled  "Science  and  Hypothe- 
sis." In  paragraph  108  we  have  already  referred  to  this 


SCIENTIFIC  THEISM  181 

work.  The  present  chapter  was  written  in  order  to  make 
this  work  available  to  a  larger  circle  of  readers  by  elimina- 
ting the  original  mathematical  analysis.  Hence  we  had  an 
opportunity  to  make  particular  mention  of  this  work  of 
Poincare.  It  affords  the  writer  exceptional  pleasure  to 
quote  the  following  from  the  above-mentioned  work  of 
Poincare : 

"But  have  we  any  right  to  admit  the  hypothesis  of  cen- 
tral forces?  Is  this  hypothesis  rigorously  accurate?  Is  it 
certain  that  it  will  never  be  falsified  by  experiment?  Who 
will  venture  to  make  such  an  assertion?  And  if  we  must 
abandon  this  hypothesis,  the  building  which  has  been  so 
laboriously  erected  must  fall  to  the  ground.  .  .  .  But 
no  system  exists  which  is  abstracted  from  all  external  ac- 
tion ;  every  part  of  the  universe  is  subject,  more  or  less,  to 
the  action  of  the  other  parts."  1 

These  statements  are  in  complete  conformity  with  the 
contentions  made  in  the  preceding  chapters  by  the  writer. 


1  Science  and  Hypothesis,  pp.  102,  103. 


CHAPTER  VIII 
ELECTROLYTIC  IONIZATION  AND  CELL  ACTION 

112.     lonization  Hypothesis. 

The  electrolytic  theory  of  dissociation  maintains  that 
molecular  system  passing  into  solution  are  separated  into 
two  kinds  of  ions  having  equal  positive  and  negative  charges. 
G.  F.  Fitzgerald  says :  "The  supposed  advantage  of  the  free 
ion  theory  is  not  only  illusory  but  misleading."  H.  E. 
Armstrong,  J.  W.  Mellor,  and  others  raise  the  following 
pertinent  objections  to  the  ionic  hypothesis : 

1.  "In  view  of  the  great  chemical  activity  of  metallic 
sodium  in  contact  with  water,  is  it  profitable  to  postulate 
the  existence  of  the  element  sodium  in  contact  with  water 
wihout  chemical  action  ?" 

Certainly  a  charged  ion  should  show,  even  in  solution, 
at  least  the  same  intensity  of  action  as  a  neutral  atom. 
Moreover,  the  free  ion  hypothesis  does  not  give  even  a  clue 
to  the  process  by  which  a  neutral  atom  becomes  a  charged 
ion  in  passing  into  solution. 

2.  "Bodies  carrying  electrical  charges  of  opposite  sign 
are  attracted  and  cling  to  one  another;  if,  therefore,  a 
mobile  solution  contains  free  and  independent  ions  carry- 
ing enormous  electrical  charges  of  opposite  sign,  how  can 
the  charged  ions  remain  more  than  momentarily  free?" 

3.  "If  an  ionized  salt,  say  sodium  chloride,  is  present 
in  solution  as  a  mixture  of  Na  (+)  and  Cl  ( — )  ions,  it 
might  be  thought  possible  to  separate  the  two  components 
by  diffusion  or  by  other  mechanical  process." 

4.  "When  a  compound  is  formed  from  its  elements, 
with  the  loss  of  energy,  the  compound  cannot  be  resolved 
into  its  elements  unless  energy  be  supplied.    It  is  therefore 
pertinent  to  inquire :    What  is  the  source  of  energy  which 
leads  to  the  fission  of  the  molecule  into  ions  carrying  equal 
but  opposite  charges  of  electricity?" 

182 


SCIENTIFIC  THEISM  183 

5.  "In  the  Hittorf  experiments  on  the  speed  of  migra- 
tion of  the  different  ions,  the  fact  observed  is  the  changing 
molecular  concentration  of  the  solution  about  the  anode  and 
cathode  during  electrolysis :  the  extraordinary  hypothesis  is 
that  during  the  passage  of  the  current  the  onions  and 
cations  move  in  the  same  electolyte  with  different  velocities, 
and  yet  the  anions  and  cations  are  given  off  at  the  respec- 
tive electrodes  at  the  same  time." 

6.  In  spite  of  the  ionic  hypothesis,  chemical  reactions 
do  take  place  in  non-conducting  solutions,  and  these  reac- 
tions are  similar  in  result  and  speed  to  those  which  occur 
in  conducting  aqueous  solutions." 

Dr.  J.  W.  Mellor  comments  upon  these  facts  as  follows : 
"The  ionic  hypothesis  cannot,  therefore,  ignore  these  ob- 
servations if  it  is  to  win  a  permanent  place  among  the  con- 
quests of  science." 

The  author  presents  the  following  hypothesis,  based 
upon  previous  conclusions,  as  a  means  of  overcoming  the 
real  and  serious  difficulties  involved  in  the  ionic  hypothesis : 

1.  All  interaction  involves  the  concomitance  of  ascend- 
ing and  descending  processes.     The  work  increments  in- 
volved in  the  former  processes  are  equal  to  the  work  decre- 
ments involved  in  the  latter.    For  each  ascending  process 
there  will  be  one  descending  process. 

2.  The  products  of  solution  appear  as  neutral  ionic 
pairs.    The  neutral  couples  result  from  the  interaction  of 
solvent  and  solute.    This  assumption  is  a  direct  corollary 
of  the  first  assumption.    Odd  solution  components  are  im- 
possible under  the  hypothesis  of  a  dual  process  involving  a 
simultaneous  and  equal  augmentation  and  degradation. 

3.  The  ions  are  capable  of  a  three-phase  change  in- 
volving two  work  steps,  equal  in  magnitude  but  opposite 
in  their  direction.    The  phase  change  in  the  neutral  energon 
is  concomitant  and  in  the  same  direction  with  the  phase 
change  in  the  ion. 

4.  The  phase  association  is  such  that  the  electron  ap- 
pears at  the  high  phase,  the  energon  at  the  neutral  phase, 
and  the  positon  at  the  low  phase. 

5.  The  algebraic  sum  of  the  work  done  in  any  system 
is  zero.    We  shall  consider  two  cases  by  way  of  illustrating 
the  application  of  our  hypothesis. 


184  SCIENTIFIC  THEISM 

113.  CASE  I.    ZINC  IN  THE  PRESENCE  OF  HYDROCHLORIC 

ACID 

Zinc  goes  into  solution,  replacing  hydrogen  and  form- 
ing zinc  chloride.  Hydrogen  gas  is  liberated.  Hydrochloric 
acid  is  in  the  neutral  phase,  hydrogen  and  chlorine  existing 
as  neutral  ions.  The  difference  of  potential  between  metallic 
zinc  (low  phase)  and  chlorine  (neutral  phase)  is  greater 
than  the  difference  in  potential  between  metallic  zinc  (low 
phase)  and  hydrogen  (neutral  phase),  therefore  metallic 
zinc  (low  phase)  goes  into  solution  on  an  ascending  grad- 
ient, becoming  ionic  zinc  (neutral  phase),  replacing  the 
ionic  hydrogen  (neutral  phase),  which  becomes  hydrogen 
gas  (low  phase)  along  a  descending  gradient.  The  algebraic 
sum  of  the  work  done  in  the  system  is  zero  because  the 
appearance  of  one  positive  work  unit  is  concomitant  with 
the  production  of  an  equal  negative  work  unit. 

114.  CASE  II.    THE  DANIELL  CELL 

Metallic  zinc  in  the  presence  of  a  solution  of  zinc  sul- 
phate. Metallic  copper  in  the  presence  of  a  solution  of 
copper  sulphate.  Mechanical  mixing  of  the  solutions  pre- 
vented by  a  porous  partition.  The  interaction  of  water  and 
zinc  sulphate  produces  the  neutral  couples,  hydroxidion 
(hydrogen  and  oxygen) ,  hydrion  (neutral  hydrogen) ;  and 
zincion  (neutral  zinc),  sulphanion  (one  atom  of  sulphur, 
four  atoms  of  oxygen) .  Similarly  the  interaction  of  water 
and  copper  sulphate  produces  the  neutral  couples,  hydrox- 
idion (one  neutral  hydrogen  and  one  neutral  oxygen  atom) , 
hydrion  (neutral  hydrogen)  ;  and  dicuprion  (neutral  cop- 
per ion) ,  sulphanion.  We  shall  use  the  subscripts  h,  n,  and 
I  to  signify  high,  neutral,  and  low  phase,  thus : 

Sulphanion  (S04)  in  the  low  phase  =   (SOJ , 
Zinc  (Zn)  in  the  neutral  phase  =  (Zn)  B,  etc. 

We  must  now  seek  the  direction  of  the  stress  relief 
gradients  in  the  systems  on  both  sides  of  the  porous  parti- 
tion. On  the  zinc  side  the  difference  in  potential  between 
metallic  zinc  (Zn) ,  (zinc,  low  phase)  and  sulphanion  in  the 
neutral  phase  (S04)  „  is  greater  than  the  difference  in 
potential  between  zinc  neutral  phase  (Zn)ft  and  (SOJB. 


SCIENTIFIC  THEISM  185 

Since  each  work  step  involves  a  constant  increment  or 
decrement  in  the  potential  difference,  it  follows  that  the 
potential  difference  between  any  two  ions  remains  con- 
stant throughout  the  phase  change.  Now  since  the  crucial 
ionic  pair  in  the  system  is  the,  (Zn-S04)  group  because 
this  involves  the  greatest  potential  difference, —  (the  pos- 
sible combinations  are  (Zn-H),  (Zn-OH),  (Zn-S04), 
(H-HO),  (H-S04),  (OH-S04),  and  (Znfl-Zn,  ),- it  follows 
that  the  group  (Zn,  -SO4)  is  the  determinant  of  the  system 
because  its  potential  difference  is  greater  than  (Zn'B-S04). 
The  difference  of  potential  between  (Zn)  a  and  (Zn),  is  an 
ultimate  unit  of  potential  difference  hence  this  group  can- 
not be  considered. 

In  the  copper  sulphate  chamber  similar  group  combina- 
tions can  be  made  by  replacing  zinc  with  copper  in  the  above 
groups.  The  combined  systems  will  strive  for  the  produc- 
tion of  a  minimum  resultant  difference  of  potential.  Con- 
sequently the  crucial  group  in  the  copper-sulphate  chamber 
is  the  group  which  involves  the  lowest  difference  in  poten- 
tial because  this  group  will  establish  the  maximum  result- 
ant potential  difference.  Now  since  the  difference  in  po- 
tential between  (Cu)w  and  (Cu),  is  one  ultimate  unit,  this 
is  the  crucial  group.  The  active  groups,  therefore,  are  the 
(Zn-S04),  (Znff-Znt),  (Cu-S04),  and  (Cun-Cu,),  and  they 
become  the  determinants  of  the  resultant  potential  differ- 
ence or  E.  M.  F.  of  the  complete  system.  Since  the  groups 
(Cua-Cu,)  and  (Zn«-Zn  )  both  involve  one  ultimate  unit 
of  potential  difference  along  oppositely  directed  gradients, 
the  former  being  descending  and  the  latter  ascending,  these 
differences  neutralize  each  other.  Hence  the  resultant 
E.  M.  F.  of  the  cell  is  determined  by  the  (Cu-S04)  and 
(Zn-S04)  groups. 

Since  (S04)  is  common  to  both  groups,  the  determina- 
tion of  the  E.  M.  F.  of  the  system  reduces  to  the  determina- 
tion of  the  potential  difference  between  (Zn)  and  Cu). 
The  well-known  procedure  is  as  follows : 

(Zn  -  SO4)  -  (Cu  -  S04) 

=  |0.50-(-2.2)J  -  1-0.60-  (2.2)|  = +2.70-1. 60= -fl.  10  volt; 
or,     Zn  —  Cu 

=  JO. 50-  (- 0.60)}  =  +  1.10  volts. 


186  SCIENTIFIC  THEISM 

That  the  osmotic  pressure  and  solution  tension  are  ulti- 
mately due  to  the  same  causes  ought  to  be  evident. 

We  show  diagrammatically,  in  Fig.  15,  the  cyclic  changes 
which  take  place  in  the  members  of  the  active  groups. 
Ascending  processes  are  represented  by  arrows  pointing 
upward,  and  descending  processes  by  arrows  pointing  down- 
ward. The  three  phases  are  represented  by  the  subscripts 
h,  n,  and  I  attached  to  the  chemical  symbols,  and  the  letter 
U  means  one  ultimate  work  unit  which  is  equal  to  the  prod- 
uct of  the  electrical  charge  and  the  ultimate  unit  of  potential 
difference.  The  notion  that  an  electrical  charge  is  an  inde- 
pendent entity  capable  of  being  attached  to  and  detached 
from  matter  involves  insurmountable  difficulties.  The 
charge  is  a  physico-mathematical  concept  crystallized  out 
of  the  content  of  an  activity  which  includes  it  and  all  other 
similar  crystallizations.  The  material  form  of  the  energy 
or  work  unit  U  is  a  three-phase  system  capable  of  passing 
through  two  work  steps.  At  the  high  phase  it  is  the 
electron,  at  neutral  it  is  the  energon,  and  at  low  it  is  the 
-positon.  For  work  to  be  done  a  change  in  phase  must  take 
place.  At  the  incipiency  of  the  action  the  members  of  the 
active  groups  are  neutral  and  the  zinc  and  copper  electrodes 
are  at  the  low  phase.  Both  members  of  every  ionic  couple 
are  affected  during  the  action.  An  ascending  process  in  one 
member  involves  a  descending  process  in  the  other.  The 
positive  work  is  always  equal  to  the  negative  work  in  the 
ionic  couple. 

The  changes  which  take  place  in  the  cell  may  be  analyzed 
into  the  following  steps  (shown  diagrammatically  in  Fig. 
15) ,  without  reference  to  an  actual  time  sequence : 

1.     (Cu)tt  descends  to  (Cu),,  (S04)  B  ascends  to  (S04)A  ; 

2.  (Cu)   is  bivalent  and  it  gives  up  two  work  units 
2U  to  the  copper  electrode. 

3.  In  the  external  circuit  2U l  (positons)    can   ascend 
to  2Uti  (energons)  doing  two  ultimate  units  of  work  along 
an  ascending  gradient. 

In  the  copper  sulphate  chamber  metallic  copper  (Cu)t 
is  deposited  on  the  copper  electrode.  We  leave  (S04)  at 
high  phase  temporarily  while  we  pass  to  the  consideration 
of  the  activities  in  the  zinc-sulphate  chamber. 


SCIENTIFIC  THEISM  187 

4.     (SO4)ft    descends    to    (S04)  ,    (Zn)ft    ascends   to 


5.  (SO4)  is  bivalent  and  it  gives  up  two  work  units 
2U  i  to  (Zn),    (metallic  zinc)  of  the  zinc  electrode. 

6.  (Zn),    ascends  to  (Zn)fi  due  to  the  addition  of  the 
two  work  units  2(Ul  toC7tt).     Migration  takes  place  and 

(Zn)*  replaces  (Cu)A. 

7.  (Zn)h  descends  to   (Zn)n   concomitantly  with  pro- 
cess number  6. 

8.  (SO4)j     ascends    to     (S04)fi    concomitantly    with 
(SO4)ft   descending  to  (SO4)  tf. 

All  the  members  of  the  active  groups  in  the  electrolytes 
have  gone  through  a  cyclic  change  from  the  initial  neutral 
phase  and  back  to  neutral.  For  every  descending  process 
there  has  been  an  ascending  process.  Two  free  positons 
(2U  t)  have  been  given  to  the  copper  electrode.  In  the 
external  circuit  these  two  units,  in  passing  from  low  to 
neutral  phase,  can  do  two  ultimate  units  of  work  along  an 
ascending  gradient.  Corresponding  to  this  ascending  pro- 
cess in  the  external  circuit,  a  descending  process  from  high 
to  neutral  will  set  in. 

Electrolytes  of  different  concentrations  in  the  presence 
of  electrodes  of  the  same  material  constitute  another  form 
of  an  unbalanced  system.  In  such  an  unbalanced  system 
ascending  and  descending  processes  will  be  established  and 
their  continuance  is  assured  until  the  concentrations  become 
the  same. 

We  have  previously  stated  that  the  concurrent  system 
may  also  be  considered  as  contained  within  the  material 
group.  This  involves  the  existence  of  neutral  energons 
within  the  cell  system.  Our  reactions  may  be  explained  from 
this  standpoint.  The  introduction  of  a  positon  into  the 
concurrent  system  disturbs  the  neutrality  of  one  energon 
because  it  is  in  the  nature  of  an  influx  of  energy  into  the 
concurrent  system.  The  energon  members  of  the  concurrent 
system  must  suffer  radial  expansion  when  positons  are 
introduced  in  order  that  the  resultant  potential  difference 
may  remain  unchanged.  One  neutral  energon  is  augmented 
into  an  electron  (high  phase)  for  each  excitant  positon  in- 
troduced into  the  concurrent  system. 


188  SCIENTIFIC  THEISM 

If  U  is  the  ultimate  unit  of  work,  then,  irrespective  of 
direction  of  the  gradient,  we  have 

U  =  (U,  to  U.)  =  (UA  to  Un)  =  (U,  to  U,)  =  (UB  to  U*). 

The  positon  is  an  ascending  process  and  may  be  re- 
garded as  positive  (-f) ,  and  it  is  equal  to  -f  U  in  magnitude. 
The  electron  is  a  descending  process  and  may  be  considered 
as  negative  ( — ),  and  it  is  equal  to  — U  in  magnitude. 

The  addition  of  a  positon  (+Z7)  to  one  member  in- 
volves the  addition  of  an  electron  ( — U)  to  another  mem- 
ber. If  a  member  is  at  high  phase,  then  we  may  regard  this 
as  being  due  to  the  application  of  a  positon  to  it  when  at 
neutral.  Similarly,  from  low  to  neutral  involves  one  posi- 
ton. The  application  of  an  electron  to  a  member  at  high 
will  bring  it  to  neutral  accompanied  by  the  liberation  of  an 
energon  which  rejoins  the  concurrent  system.  The  ap- 
plication of  an  electron  to  a  member  at  neutral  reduces  it  to 
low,  with  the  liberation  of  a  positon.  After  all,  this  is  merely 
another  way  of  considering  ascending  and  descending  pro- 
cesses, the  results  being  identical. 

The  cell  actions  may  be  set  forth  in  terms  of  the  follow- 
ing reactions : 


f(Cu) 
l(S04 


-  In  the  Copper-Sulphate  Chamber 

— 2U  =  (Cu)  i+2  Free  Positons.     Copper  deposited. 

)n+2U=(S04)h. 


The   two   free   positons   pass   by   way   of   the   copper 
electrode  to  the  external  circuit. 

In  the  Zinc-Sulphate  Chamber 

|(SO4)n  —  2U  =  (SO4)i+2   free    positons     which    are   given 

2 .  <  up  to  metallic  (Zn)  [  of  the  electrode. 
((Zn)n+2U  =  (Zn)h. 

/"(Zn)i    (metallic) +2U  =  (Zn)n    (ionic)    metallic    zinc   goes 

3 .  /  into  solution. 
((Zn)h-2U  =  (Zn)n. 

This  leaves  (SO4)h    in  the  copper-sulphate  solution  and 
(SO4)(,  in  the  zinc-sulphate  solution. 


SCIENTIFIC  THEISM  189 

The  external  circuit  must  liberate  two  positons  (+2U) 
for  the  two  received,  and  these,  when  they  enter  the  cell, 
augment  two  energons  in  the  concurrent  system  into  elec- 
trons (  —  2U)  ,  hence  the  cycle  is  completed  by  the  following 
reactions  : 

((SO4)  i+2U  (from  external  circuit)  =  (SO4)n. 
4.     <(SO4)h—  2U     (concurrent     electrons)  =  (SO4)n  -{-liberation 
'  of  two  energons  back  into  the  concurrent  system. 

Summation  of  U  Values 

It  is  seen  that  the  algebraic  sum  of  the  U  values  in  the 
above  four  steps  is  equal  to  zero. 

115.     Work  of  Decomposition. 

Suppose  a  battery  of  these  cells  is  used  to  send  a  current 
into  a  solution  of  hydrochloric  acid  (HCl)  in  order  to  decom- 
pose it.  The  two  members  H  and  Cl  of  the  ionic  couple  are 
neutral,  being  in  solution.  For  every  positon  (-|-U)  in- 
troduced into  this  system  an  electron  (  —  U)  is  formed  in  the 
concurrent  system.  When  a  positon  is  added  to  one  mem- 
ber of  the  couple  a  concurrent  electron  is  added  to  the  other. 
Now  since  (H)  and  (Cl)  are  both  univalent,  we  may  write 
the  reactions  as  follows  : 


(CJl)tr  —  U  =  (Cl){     -|~  the  liberation  of  one  positon. 

This  leaves  (H)  and  (Cl)  at  high  and  low  phases  re- 
spectively, with  one  work  step  U  intervening  to  neutral  for 
each.  The  electric  current  consists,  then,  in  a  flow  of  posi- 
tons in  one  direction,  and  the  generation  of  electrons  from 
energons  in  the  concurrent  system  and  their  flow  in  the  op- 
posite direction  —  positon  through  electrons.  Mechanical 
energy  expended  in  the  current  generator  produces  electrons 
from  energons  with  the  concurrent  compensating  production 
of  positons.  The  cell  process  liberated  positons,  with  the 
concurrent  production  of  electrons  in  the  concurrent  system. 
Activity  manifest  as  primary  matter  or  energons  becomes 
secondary  matter  manifest  as  positons  and  electrons;  and 
matter  is  merely  a  phase  of  activity. 


190 


SCIENTIFIC  THEISM 


Externa 

/  Circuit. 

C®  }->- 

'    uh 

Copper 

Copper  Sulphate 

ZLinc  Qulphate. 

Zinc, 

Electee 

•Sotu  tion  . 

Solution. 

Electrode 

To 

External 
Circuit. 

*"'\ 

(Cu)n                         ^ 

1  »             '/9 

1 
(SCLJL 

i  . 

(Zn)n        1 

L  .•*»* 

zu* 

• 
(Cu) 

T                 2Un 
\  —\('* 

:: 

(SQffo 

o       1 

(SO) 

L 

® 

CHAPTER  IX 
THE  FOUR  WORLDS 

116.     Resume 

In  this  work  we  have  dealt  with  interaction  in  the  phys- 
ical universe.  We  have  found  that  things  are  interdepend- 
ent and  not  independent.  In  their  totality  they  constitute  a 
unitary  cosmos.  The  ultimates  of  things  are  action  centers. 
These  action  centers  manifest  in  space  and  time  in  accord- 
ance with  the  deterministic  dictates  of  their  God-given  char- 
acteristics or  endowments.  The  uniformities  of  physical  ac- 
tion may  be  described  in  terms  of  natural  laws.  Nodal  devia- 
tions from  finite  and  partial  uniformity  are  teleological  re- 
sultants which  are  in  complete  conformity  with  the  prin- 
ciple of  non-contradiction.  Space  and  time  are  forms  of  ap- 
prehension possessing  both  objective  and  subjective  signif- 
icance. Because  space  and  time  are  not  things,  it  does  not 
follow  that  they  are  unreal.  If  a  certain  type  of  action  oc- 
curs when  the  distance  between  two  things  is  small,  and 
when  the  distance  is  increased  this  action  fails  to  occur,  it 
does  not  follow  that  space  or  distance  is  an  action-prohibit- 
ing entity.  All  that  follows  from  this  fact  is  that,  because 
of  the  change  in  distance,  new  arrangements  of  the  activity 
factors  have  been  established  by  the  change  in  the  relative 
location  of  the  things.  A  change  in  location  involves  a 
variation  of  the  quantum  of  the  intervening  concurrent  sys- 
tem together  with  a  change  in  the  total  action  setting.  If 
a  certain  type  of  action  fails  to  appear,  we  attribute  the  fail- 
ure to  this  new  action  setting  and  not  to  any  prohibitive 
action  of  an  independent  spatial  entity.  We  have  seen  that 
physical  action  ultimately  depends  upon  the  sustaining  in- 
fluence of  the  Being  of  God.  We  look  upon  the  universe  as 
due  to  a  free  creative  act  of  God.  We  think  of  God  as  both 
Immanent  in  the  cosmos  and  Transcendent  above  its  finite 
limitations.  We  find  both  purpose  and  teleology  in  the  uni- 

191 


192  SCIENTIFIC  THEISM 

verse,  and  we  regard  both  as  phases  of  the  principle  of  non- 
contradiction. 

The  scope  of  this  work,  being  limited  to  the  physical 
universe,  prohibits  a  discussion  of  its  relation  to  the  worlds 
of  consciousness  and  subconsciousness.  However,  we  shall 
briefly  outline  the  direction  which  the  logical  development 
of  our  position  must  take  when  the  worlds  of  consciousness 
and  subconsciousness  are  included  within  the  created 
cosmos. 

117.     The  World  of  Subconsciousness. 

The  stream  of  consciousness  flows,  as  it  were,  between 
two  banks :  one  the  world  of  activity,  matter,  and  life ;  the 
other  the  world  of  subconsciousness.  The  subconscious 
world  is  a  vast  region  comparatively  unexplored  and  little 
understood.  The  bulk  of  conscious  and  unconscious  experi- 
ence is,  as  it  were,  filed  away  in  the  eternal  vaults  of  this 
wonderful  world.  Under  certain  abnormal  conditions  the 
vaults  are  opened  and  the  stored  information  is  again  re- 
vealed to  conscious  minds.  The  subconscious  world  is  the 
background  of  our  conscious  activity,  and  few  are  those  who 
have  not,  in  some  moment  of  their  life,  been  in  rapport  with 
the  groundwork  of  conscious  life.  The  extent  of  this  rap- 
port is  only  a  question  of  degree ;  in  some  individuals  it  is 
more  marked  than  in  others.  In  passing  from  the  sub- 
conscious to  the  conscious,  reality  is  differentiated  into 
temporal  series  and  spatial  appearance  through  the  forms 
of  conscious  apprehension.  Looking  through  the  binocular 
of  space  and  time,  the  finite  self  sees  reality  as  the  moving 
film  of  life,  the  present  receding  into  the  past  and  the  future 
moving  into  the  present.  The  binoculars  of  space,  time,  and 
causality  would  fail  us  in  our  differentiation  of  the  world 
of  reality  unless  the  distinctions  possessed  objective  signif- 
icance. The  finite  selves  are  free  factors  in  the  making  of 
the  film  of  reality.  At  the  same  time  we  are  being  molded 
and  formed  through  interaction  with  the  other  constituents 
of  reality.  Our  pilgrimage  from  the  most  remote  of  the 
world  projections  leads  us  back  to  God  our  Creator.  The 
principle  of  non-contradiction,  arising  from  the  Being  of 
God,  like  the  fountain  stream  projected  high  into  the  atmos- 
phere and  into  the  utmost  regions  of  existence,  unifies  the 


SCIENTIFIC  THEISM  193 

contradictions  of  all  finite  existence,  harmonizing  finite  be- 
ing with  the  Reality  of  the  Infinite  Creator. 

118.     The  Inorganic  World. 

The  inorganic  world  is  the  world  of  physical  determin- 
ism and  natural  law.  By  natural  law  we  do  not  mean  some 
external  governing  entity  alien  to  things,  but  we  mean  that 
consistent  rational  record  of  the  action  of  things  which  to 
us  appears  as  laws  and  for  things  is  a  partial  account  of 
the  manner  of  their  interaction.  In  the  inorganic  world 
the  interaction  relations  between  the  physical  centers  is 
equivalent  to  a  well-defined  sensitiveness  of  each  center  to 
the  rest  which  constitute  its  environment.  The  magnitude 
of  this  sensitiveness  grows  as  the  action  groups  become 
more  complex.  The  sphere  of  interaction  increases  with 
this  growth  in  sensitiveness.  From  monon  to  mind,  the 
growth  is  continuous.  This  constitutes  the  essence  of  evo- 
lution. By  this  statement  we  do  not  mean  that  all  forms 
of  existence  are  developments  from  one  existence  type.  The 
great  complexity  of  the  universe  points  to  a  great  diversity 
of  beginnings.  The  attempted  unifications  and  simplifica- 
tions of  the  various  evolutionary  schools  are,  for  the  most 
part,  total  failures  because  they  do  not  begin  to  do  jus- 
tice to  the  complexity  of  the  cosmos.  In  the  inorganic 
world  there  is  no  genuine  freedom  in  the  sense  of  the 
possibility  of  a  new  creation  which  augments  the  world 
content  and  the  free  individual. 

All  change  is  an  exchange  or  interchange  according  to 
natural  law  in  this  purely  physical  world.  The  only  free- 
dom we  find  in  the  inorganic  world  is  the  freedom  of  ex- 
hibiting that  given  and  fixed  character  of  the  action  center 
which  lies  at  the  foundation  of  natural  law.  This  constant 
display  of  fixed  character  is  called  "determinism."  Free- 
dom and  determinism  are  not  incompatible.  In  the  con- 
scious world  freedom  would  result  in  chaos  unless  exercised 
within  the  boundaries  of  physical  determinism.  Thought 
activities  would  be  ineffective  unless  focused  upon  an  en- 
vironment which  may  be  defined  in  terms  of  principles  and 
laws.  Thought  as  free  will  could  find  no  point  from  which 
to  initiate  action,  with  even  the  remotest  assurance  of  a 
definite  result,  unless  the  physical  world,  the  environment, 


194  SCIENTIFIC  THEISM 

could  be  relied  upon  to  react  in  a  definite,  determinable 
manner. 

119.     The  Organic  World  and  the  Entity  of  Life. 

In  the  inorganic  world  all  is  mechanism  as  far  as 
phenomenal  appearance  is  concerned.  As  the  created  work 
of  God,  the  inorganic  world  is  more  than  mechanism,  for 
God  expresses  His  Eternal  Reality  in  the  inorganic  world  by 
His  Immanence  in  conjunction  with  His  Eternal  Transcend- 
ence. Consequently  the  inorganic  world  is  more  than  a  mere 
machine.  For  this  reason  science  cannot  explain  the  physical 
universe  in  terms  of  mechanism  alone.  In  one  sense  of  the 
word,  the  monon  is  an  individual  if  separateness  or  dis- 
creteness is  all  that  is  meant  by  individuality.  Mere  dis- 
creteness, however,  is  not  a  criterion  of  genuine  individ- 
uality, for  it  conveys  the  implication  of  being  a  part  of  a 
larger  totality  which  itself  may  constitute  a  real  individual 
if  the  system  is  an  interacting  unity,  as  we  have  been  forced 
to  assume.  A  contentless  number  is  a  mere  mathematical 
abstraction.  Consequently  the  number  one  is  not  a  real 
unity  because  it  is  a  conceptual  abstraction  devoid  of  con- 
tent. Unity,  then,  is  continuity  of  activity,  a  persistence  of 
exhibition  of  definite  characteristics  throughout  a  multiplic- 
ity of  change.  This  idea  of  unity  does  not  involve  the  neces- 
sity of  discrete  physical  parts,  for  continuity  throughout 
change  is  the  essence  of  unity.  This  is  the  type  of  unity 
exhibited  by  the  soul.  It  does  not  follow  that  because  the 
soul  is  not  composed  of  discrete  parts  it  is  a  mere  mathe- 
matical abstraction.  The  soul  is  a  higher  form  of  unity 
whose  activity  content  is  manifold.  The  life  entity  is  a 
unity  of  the  same  order  as  the  soul  entity.  The  distinction 
between  these  two  types  of  unitary  entities  is  to  be  found 
more  in  degree  than  in  type  or  kind.  The  fact  that  the  life 
and  soul  entities  are  unities  of  a  higher  order  than  the 
merely  physical  unities  does  not  preclude  the  conjunction  of 
these  unities  into  resultant  unities  of  another  order,  for  we 
have  already  shown  that  unity  devoid  of  multiplicity 
is  a  mere  mathematical  abstraction.  We  hold  that  the 
phenomena  of  life  and  consciousness  have  not  been  and  can- 
not be  explained  by  any  system  of  philosophy,  no  matter 


\ 
SCIENTIFIC  THEISM  195 

how  subtle  in  its  excruciating  verbosity,  which  tries  to 
merge  the  three  essences  of  cosmic  reality — that  is,  the 
physical  essence,  the  life  essence,  and  the  soul  essence — into 
one  primordial  parent  entity  type  which  is  capable  of  de- 
veloping or  evolving  into  the  higher  types  through  interac- 
tion in  an  environment  composed  of  nothing  but  these  same 
primordial  existence  types.  This  is  exactly  what  modern 
philosophical  evolution  tries  to  do.  The  attempt  is  an 
ignominious  failure.  Differences  cannot  arise  out  of  same- 
ness. If  we  place  one  hundred  marbles  in  a  box  and  shake 
them  with  utmost  vigor,  we  get  nothing  other  than  one  hun- 
dred marbles  for  our  effort.  Our  effort  does  not  produce 
one  apple  even  if  we  add  another  hundred  marbles  to  the 
original  number.  This  popular  modern  intellectual  mania 
seems  to  break  out  continuously  in  an  attempt  to  evolve  the 
complex  all  out  of  the  simple  one.  This  intellectual  mania 
is  such  a  common  malady  that  he  who  refrains  from  join- 
ing these  modern  scientific  dervishes  is  charged  with  being 
simple-minded  and  demented.  We  maintain  that  religious 
intuition  is  nearer  to  the  truths  of  ultimate  reality  than  all 
the  subtle  speculations  of  these  modern  sophists.  We  con- 
tend that  the  organic  center  is  a  resultant  unity  arising 
through  conjunction  and  interaction  between  the  life  center 
and  suitable  aggregates  of  inorganic  centers.  We  extend 
the  principle  of  interaction  to  the  organic  world.  In  the 
monons  we  find  basic  fundamental  characteristics  common 
to  all.  Nevertheless,  we  recognize  differences  in  the  char- 
acteristics of  the  monons.  The  physical  universe  cannot 
be  generated  out  of  mere  number.  Similarly  we  recognize 
differences  in  the  life  ultimates.  We  shall  give  the  name 
vitons  to  these  life  ultimates.  Like  the  monons,  the  vitons 
are  capable  of  exhibiting  positive  and  negative  action 
phases  in  conformity  with  the  principle  of  non-contradiction. 
Throughout  all  the  worlds  of  being,  this  differentiation  of 
unity  into  a  positive  and  a  negative  phase  is  found.  In 
the  conscious  world  we  find  the  unity  differentiated  into 
pleasure  and  pain,  good  and  evil,  truth  and  error.  In  the 
organic  world  the  center  is  responsive  to  the  modeling  in- 
fluence  of  environment  and  it  exhibits  the  rudiments  of 
individuality. 


196  SCIENTIFIC  THEISM 

120.     The  Conscious  World  and  the  Entity  of  Soul. 

The  problem  of  operation,  control,  and  interaction  is 
more  difficult  when  we  ascend  the  thermometer  of  organized 
life  and  reach  the  more  complex  groups.  In  the  more  com- 
plex groups  we  find  the  nervous  systems  whose  f  unctionings 
provide  for  the  handling  of  the  mechanical  problems  in- 
volved in  the  operation  and  control  of  the  bodily  move- 
ments, thus  making  possible  the  representation  and  real- 
ization of  such  desires  and  interests  as  tend  toward  the 
further  development  of  a  harmonic  individuality.  In  the 
highest  organic  complexity,  the  human  body,  we  find  con- 
sciousness fully  developed.  The  conscious  being  is  a  re- 
sultant unity  arising  through  the  conjunction  and  interac- 
tion between  the  soul  and  suitable  aggregates  of  organic 
centers.  Thus  the  principle  of  interaction  is  extended  to 
the  world  of  consciousness.  Creation  did  not  cease  when 
God  created  the  physical  universe.  Free  creation  is  dis- 
tinctive of  conscious  life;  in  fact,  it  is  one  of  its  highest 
forms  of  expression.  Our  concept  of  God  must  therefore 
include  creation  as  an  abiding  form  of  expression  of  the 
infinite  Being.  God's  Immanence  and  Transcendence  as- 
sure the  continuous  responsive  expression  of  His  Free 
Creation  in  the  cosmos.  The  creation  of  souls  is  an  ex- 
pression of  the  Infinite  and  Non-Temporal  Being  of  God 
manifest  and  immanent  in  the  finite  world  of  space,  time, 
and  secondary  causation.  The  resultant  unitary  being 
which  is  produced  by  the  conjunction  and  interaction  of 
the  soul  with  the  organic  system  develops  into  complete 
consciousness  contemporaneously  with  the  observable  de- 
velopment of  the  organic,  nervous,  and  brain  structure. 
In  the  conscious  world  individuality  begins  to  assert  itself 
in  a  pronounced  and  distinct  manner  by  attempting  to  re- 
construct its  environment.  This  attempt  is  a  primary 
manifestation  of  the  will.  Moreover,  there  is  noticeable  an 
attempt  to  interpret  environment,  and  this  constitutes  the 
beginning  of  knowledge  or  cognition.  This  is  what  we  call 
mentality,  and  thus  arises  the  unitary  world  of  mind,  which 
may  be  differentiated  into  thought  as  will  and  thought  as 
cognition.  Introspection  separates  mental  activity  into  the 
two  principal  components,  will  and  cognition.  In  reality 
they  are  never  found  divorced.  Sometimes  will  appears  to 


SCIENTIFIC  THEISM  197 

be  on  the  crest  of  mind  life,  at  other  times  it  is  cognition, 
but  this  appearance  of  dualism  is  due  to  the  ineffectual  at- 
tempts of  mind  to  catch  all  of  itself  in  one  single  moment 
of  time.  Mechanism  becomes  the  servant  of  consciousness 
with  the  development  of  the  unitary  being.  Consciousness 
demands  the  performance  of  certain  movements  with  the 
minimum  of  effort.  The  nervous  system,  begining  as  mere 
reaction  to  the  simplest  stimuli,  develops  into  a  complex 
mechanism  in  accordance  with  the  requirements  of  soul  life. 
Soul  life  and  physical  mechanism  blend  into  one  unitary 
life,  and  perfect  interaction  exists  in  all  the  stages  of  de- 
velopment. Conscious  soul  life  is  the  non-spatial  phase  of 
the  life  of  mind ;  the  neural  processes  are  the  spatial  mani- 
festations of  that  activity.  The  brain  and  the  nervous  sys- 
tem are  like  the  cutting  edges  of  the  two  blades  of  a  pair 
of  shears.  Whenever  the  psychical  movement  is  effective 
within  the  world  of  space  and  time  there  the  cutting  edges 
are  in  action.  The  interacting,  moving  content  of  the  soul 
life  propels  the  action  in  a  direction  which  is  the  resultant 
of  this  soul  content.  Genuine  freedom  means  that  activ- 
ity is  given  its  course  from  the  organized  soul  content. 
Thought  as  will  produces  new  thought  solutions  tending 
toward  action.  Thought  as  cognition  produces  new  thought 
creations.  Both  thought  as  will  and  thought  as  cognition 
are  phases  of  the  unitary  life  of  the  soul, 

121.     Relation  Between  the  Conscious  and   the  Subconscious 

Worlds. 

The  interaction  between  the  soul  and  its  organic 
mechanism  may  vary  in  intensity.  When  the  interaction  is 
sharply  defined  and  of  the  maximum  intensity,  then  con- 
scious awareness  is  at  its  highest  level.  There  is  also  a 
lowest  level  corresponding  to  that  minimum  intensity  of 
interaction  which  is  capable  of  producing  conscious  aware- 
ness. These  limits  themselves  may  vary  because  of  other 
interaction  conditions.  However,  conscious  life  may  be  said 
to  be  bounded  by  a  high  and  a  low  level  of  interaction.  Be- 
low the  low  level  we  have  the  subconscious  life  of  the  soul. 
There  the  results  of  intense  interaction — that  is,  conscious 
life — are  stored  for  all  eternity.  There  the  precipitates  of 
all  conscious  activity  are  preserved  as  the  everlasting  rec- 


198  SCIENTIFIC  THEISM 

ords  of  temporal  life.  We  may  say,  then,  that  soul  life  has 
a  transcendent  and  an  immanent  phase.  The  immanent 
phase  corresponds  to  the  conscious  life,  while  the  trans- 
cendent phase  corresponds  to  the  subconscious  life.  In  this 
respect  the  life  of  the  soul  is  somewhat  similar  to  the  Life 
of  God.  One  important  difference  lies  in  the  fact  that  the 
soul  did  not  create  its  organic  mechanism.  There  is  one 
striking  similarity,  that  is,  the  Life  of  God  does  not  depend 
upon  the  continued  existence  of  the  cosmos  which  He  cre- 
ated, and  the  life  of  the  soul  continues  after  dissociation 
with  the  organic  mechanism.  We  know  very  little  concern- 
ing subconscious  interaction.  Many  indications  point  to 
the  fact  that  the  soul  is  capable  of  subconscious  interac- 
tion, but  we  know  little  of  the  modus  operandi.  The  sub- 
conscious content  may  be,  as  it  were,  the  glass  through 
which  the  soul  sees  God  dimly.  The  religious  intuition  of 
the  primitive  is  not  mere  superstition.  It  is  grounded  in 
a  deeper  reality  than  superstition.  The  universality  of  the 
religious  intuition  points  to  a  common  background  of  con- 
scious soul  life ;  that  is,  the  subconscious  soul  content.  Thus 
man  is  truly  made  in  the  Image  of  God. 

122.    The  Categories  of  Reality. 

Reality  may  be  distinguished  as  Absolute  and  Relative. 
These  two  manifestations  are  not  isolated  and  estranged 
existence  types  constituting  alien  dualistic  principles  hav- 
ing no  binding  ties  or  interrelations.  True  unity  is  brought 
about  only  through  interrelations.  In  this  sense,  therefore, 
the  Absolute  Reality  and  the  Relative  Reality  constitute  a 
unity  despite  the  fact  that  they  are  not  identical.  A  unity 
which  merges  the  Absolute  into  the  Relative  or  the  Rela- 
tive into  the  Absolute  cannot  be  constructed  philosophic- 
ally except  by  resorting  to  the  idea  of  interrelations  between 
multiplicity,  which  then  merges  multiplicity  into  unity.  If 
it  is  thought  that  the  word  "unity"  lends  profundity  to 
philosophic  contemplation,  then  we  have  as  much  right  to 
claim  unity  for  our  two  types  of  reality  as  those  phil- 
osophers who  attempt  to  remove  any  distinction  between 
these  two  types.  There  must  be  differences  in  the  content 
of  multiplicity  if  a  real  unity  can  be  established.  A  unity 
without  distinctions  and  variations  in  its  content  is  a  mere 


SCIENTIFIC  THEISM  199 

mathematical  abstraction.  Hence  we  maintain  that  our 
position  is  no  more  dualistic  than  that  of  the  most  subtle 
monist  whose  principal  endeavor  it  is  to  merge  multiplicity 
into  unity.  The  monist  denies  that  his  endeavor  results  in 
an  identity,  nevertheless  he  charges  us  with  gross  lack  of 
philosophic  insight  and  acumen  whenever  we  apply  his  own 
procedure  to  a  content,  grounded  in  fact,  which  will,  when 
developed  to  its  logical  conclusion,  exhibit  a  genuine  re- 
ligious value.  We  speak  of  reality  as  relative  in  order  to 
emphasize  the  fact  that  it  owes  its  significance  to  the  Ab- 
solute Reality — God.  Moreover,  Relative  Reality  is  rela- 
tive by  virtue  of  genuine  and  real  relations  to  God.  We 
may  formulate  the  categories  of  reality  as  follows: 

ABSOLUTE  REALITY 
GOD 

A  Timeless  Transcendent  Reality,  Immanent  in 
Temporal  Finiteness 

The  Absolute  is  non-spatial,  non-temporal,  and  capable 
of  Absolute  Free  Origination.  God  is  therefore  the  Pri- 
mary Causation  in  distinction  to  Secondary  Causation, 
which  manifests  in  finiteness  in  conjunction  with  the 
forms  of  space  and  time.  God  is  Absolute  Truth,  Abso- 
lute Freedom,  and  Perfection;  therefore  His  Omniscience 
and  Omnipotence  follow  as  logical  consequents.  God  is  the 
Absolute  Creative  Being. 

RELATIVE  REALITY 
7.     The  Inorganic  World 
The  inorganic  world  is  subdivided  into: 
1.     The  Primary  World,  composed  of: 

a.  Monons,    the    primordial    form    of    activity 

centers. 

b.  Energons,  the  gyratory  groups  composed  of 

monons. 

These  gyratory  energons  constitute  our  concurrent  sys- 
tem of  primary  matter  which  interacts  with  secondary 
matter  in  the  production  of  physical  phenomena.  The 
energons  are  the  neutral  phase  of  matter. 


200  SCIENTIFIC  THEISM 

2.     The  Secondary  World,  composed  of 

a.  Electrons,  the  negative  phases  of  the  energons. 

b.  Positons,  the  positive  phases  of  the  energons. 
These  groups  constitute  the   excitant  system  of  sec- 
ondary matter  which  generates  physical  phenomena  through 
interaction  with  the  concurrent  system  or  primary  neutral 
matter.     Complex  material  aggregates  are  built  up  from 
these  secondary  elementals. 

Principal  Characteristic  of  the  Inorganic  Centers 

1.  Capable  of  self-maintenance. 

2.  Capable  of  definite  physical  combinations. 

3.  Limited     or     deterministic     sensitiveness     to     en- 
vironment. 

4.  No  genuine  creative  freedom. 

5.  Differing  in  many  characteristics. 

II.     The  Organic  World 
We  subdivide  the  organic  world  into: 

1.  Primary  Activity  composed  of  Vitons  manifesting 
the  Principle  of  life.     The  Vitons  are  the  Life  Ultimates. 
We  may  say  that  the  Vitons  are  elementary  Souls  lacking 
that  potentiality  which  insures  development  into  the  highest 
form  of  conscious  life.    The  Vitons  differ  in  many  of  their 
fundamental  characteristics.    All  Vitons  manifest  the  Prin- 
ciple of  Life  given  to  them  by  a  creative  act  of  God,  who  is 
the  Source  of  Life.    God's  ever  present  Immanence  insures 
to  every  organism  an  elementary  soul  or  viton  which  is  in 
harmony  with  its  being. 

2.  A  Secondary  Activity  composed  of  groups  of  vary- 
ing complexity  built  up  of  secondary  matter.    The  organic 
molecular  groups  are  generally  very  complex. 

The  resultant  unitary  organic  center  is  due  to  the  con- 
junction and  interaction  of  the  Primary  Activity  of  the 
Viton  and  the  Secondary  Activity  of  Secondary  Matter.  Be- 
cause of  its  content  of  secondary  matter,  the  organic  center 
can  interact  with  primary  matter. 

Principal  Characteristics  of  the  Organic  Center 

1.  Capable  of  self -maintenance. 

2.  Capable  of  definite  physical  combinations. 

3.  A  greater  sensitiveness  to  environment. 


SCIENTIFIC  THEISM  201 

4.  Capable  of  exhibiting  an  indeterminate  creative  im- 
pulse ;  that  is,  limited  freedom. 

5.  Differing  in  many  characteristics. 

///.     The  Conscious  World 
The  conscious  world  may  be  subdivided  into : 

1.  A  Primary  Activity  composed  of  Souls  manifesting 
the  Principle  of  Free  Individuality.     Herein  lies  the  dis- 
tinction between  the  Soul  and  the  Viton.     The  soul  is  of 
God  through  His  act  of  creation. 

2.  A  Secondary  Activity  composed  of  highly  developed 
organic  systems  capable  of  minute  shades  of  responsive 
interaction. 

The  resultant  unitary  conscious  center  arises  through 
conjunction  and  interaction  of  the  soul  with  its  organic 
system.  Development  is  not  precluded  by  this  interaction, 
but,  on  the  contrary,  it  is  fostered  by  it.  The  modeling 
influence  of  environment  is  included  as  a  fact  due  to  gen- 
eral interaction. 

Principal  Characteristics  of  the  Conscious  Center 

1.  Capable  of  self -maintenance. 

2.  Capable  of  definite  physical  combinations. 

3.  A  highly  attuned  sensitiveness  to  environment. 

4.  Capable  of  reconstructing  its  environment.     This 
tendency  constitutes  the  basic  root  of  the  will. 

5.  Capable  of  producing  new  thought  solutions  tend- 
ing toward  action.    This  is  thought  as  will. 

Results  in  the  production  of  the  moral  structure. 

6.  Capable  of  interpreting  its  environment.    This  ten- 
dency constitutes  the  basic  root  of  cognition. 

7.  Capable  of  producing  new  thought  creations.    This 
is  thought  as  cognition.    Results  in  the  production  of  art, 
literature,  science,  and  philosophy. 

8.  Capable  of  expressing  a  more  complete  individuality 
through  the  exercise  of  a  freedom  which  is  only  partially 
limited  by  the  necessary  conditions  of  action  imposed  by 
environment. 

IV.     The  Subconscious  World 
We  may  differentiate  soul  life  into : 

1.  A  Primary  Activity  consisting  in  the  soul  life  below 
the  lowest  level  of  consciousness. 


202  SCIENTIFIC  THEISM 

2.  A  Secondary  Activity  consisting  in  the  conscious  life 
brought  about  by  interactions  between  the  soul  and  the 
organic  system  above  the  lowest  level  of  consciousness. 

The  subconscious  world  pertains  to  the  primary  activity 
of  soul  life.  Although  the  content  of  this  primary  or  sub- 
conscious activity  is  for  the  greater  part  conjectural,  never- 
theless we  have  a  quantum  of  evidence  which  at  least  indis- 
tinctly indicates  some  phases  of  this  hidden  content.  It  is 
highly  probable  that  this  subconscious  phase  of  soul  activity 
is  capable  of  and  includes  within  its  content: 

1.  The  indestructible  record  of  perceptions,  conscious 
thoughts,  and  acts. 

2.  Producing  the   so-called  abnormal  psychical   phe- 
nomena. 

3.  Interaction     with     other     primary     subconscious 
activities. 

4.  Projecting  portions  of  its  content  above  the  lowest 
level  of  consciousness  under  suitable  conditions  of  inter- 
action. 

5.  Receiving  certain  types  of  direct  or  intuitive  knowl- 
edge and  revelation. 

6.  The  groundwork  of  instinctive  responsiveness. 

7.  The  groundwork  of  the  intuitions  of  religion  and 
faith  in  an  ethical  order. 

123.     Chance  and  Predetermination. 

Is  life  a  mere  rattling  of  the  chains  of  finite  serfdom? 
Are  the  links  in  the  chain  of  life  forged  before  our  advent 
into  the  arena  of  finite  existence?  If  we  reject  this  view, 
are  all  events  merely  the  chaotic  outcome  of  chance  and  con- 
tingency? We  take  the  position  that  both  these  views  are 
erroneous  because  they  are  the  extremes  of  a  view  which 
includes  a  modified  interpretation  of  both.  In  creative 
art  we  find  the  essence  of  a  genuine  freedom.  Conscious 
life  cannot  be  predicted  with  any  greater  certainty  than  art, 
which  owes  its  novelty  to  the  mental  content  and  depth  of 
penetration  of  the  artist's  mind.  Art  owes  its  existence  to 
the  initiative  and  creative  constructiveness  of  the  artist. 
This  is  all  that  can  be  asked  for  freedom.  If  environment 
is  the  only  factor  in  the  making  of  an  individual,  then  two 
minds  in  the  same  environment  should  be  as  like  as  two 


SCIENTIFIC  THEISM  203 

peas  in  a  pod.  We  do  know,  however,  that  in  the  same  home 
two  children  carve  out  different  mental  worlds  for  them- 
selves from  the  same  environment.  Without  freedom's 
creative  impulse,  the  conscious  world  would  show  but  little 
diversity.  True,  you  will  grant,  but  individual  differences 
are  themselves  factors  that  are  predetermined  and  as  such 
have  previously  existed  somewhere.  In  other  words,  no 
really  new  element  is  to  be  found  in  the  entire  realm  of  con- 
scious life.  This  is  a  fatalism  which  chains  the  soul  to 
eternal  serfdom.  A  past  which  is  a  genuine  past,  and  as 
such  does  not  exist,  can  have  no  determinate  influence  upon 
the  present  in  producing  the  future.  Given  the  artist  and 
his  mental  content,  no  one  can  predict  the  nature  of  the 
work  of  art.  The  result  is  a  genuine  novelty,  unaccountable 
and  unpredictable.  If  all  the  mental  content  is  known  to  a 
greater  mind,  then  only  is  prediction  possible.  We  can 
mean  nothing  less  by  prediction  than  that  certain  results 
have  been  brought  about  before  they  can  be  observed  as  phe- 
nomenal facts.  Even  in  the  realm  of  logic  the  creative 
principle  of  freedom  reforms  a  world  content  into  startling 
and  novel  combinations.  The  physical  world  in  which  we 
live  is  a  world  of  determinism,  understandable  in  terms  of 
natural  laws.  The  mechanistic  elements  of  our  body  belong 
to  the  world  of  determinism. 

This  constitutes  the  physical  logic  of  the  universe.  With- 
out this  background,  rational  action  is  impossible.  A  knowl- 
edge of  this  world  of  predictable  and  definite  consequences 
is  part  of  the  content  of  mind  gained  through  interaction 
with  environment.  All  we  can  ask  is  our  share  in  the  crea- 
tive activity  of  a  world  which  includes  physical  deter- 
minism. This  is  the  only  form  in  which  predetermination 
enters  as  an  influencing  element  in  our  creative  activity. 
In  fact,  creative  activity  requires  this  known  and  definite 
foundation  for  its  expression  and  realization.  Our  soul 
content  is  the  fountain  from  which  action  arises.  Although 
action  is  dependent  upon  mind  content,  nevertheless  the  soul 
is  able  to  originate  and  create  new  thought  and  action 
departures.  The  chance  element  is  in  the  nature  of  an 
opportunity  to  originate  and  initiate.  Chance  as  a  chaotic 
contingency  is  not  found  in  the  world  of  consciousness.  All 
action  proceeds  from  the  content  of  the  self.  The  new  does 


204  SCIENTIFIC  THEISM 

not  arise  from  chaos,  but  from  the  cosmos  of  the  self.  Love 
and  logic  find  no  room  in  fatalism,  that  dark  hand  from  a 
remorseless  beyond,  which  drags  the  self  hither  and  thither 
with  predetermined  precision,  calculated  by  the  infernal 
master  mind  of  a  being  inimical  to  all  forms  of  genuine 
self-expression.  Fatalism  annihilates  individuality.  The 
two  cannot  exist  together.  A  thing  whose  movements  are 
prearranged  and  controlled  is  not  an  individual,  but  a 
machine.  At  the  time  of  the  act  it  (the  act)  is  characteris- 
tic of  the  self  which  then  exists.  The  act  is  a  deputy  of  the 
soul  content  which  brings  it  into  being.  Freedom  does  not 
mean  that  you,  being  what  you  are  at  this  moment,  can 
act  in  a  manner  which  differs  from  the  resultant  of  your 
momentary  mind  content.  You  are  what  your  action  re- 
sponses (reactions)  to  an  active  environment  have  made 
you.  You  may  become  a  radically  different  self  due  to  your 
last  act.  Your  self  is  not  a  static  thing;  it  is  a  dynamic 
action  center  changing  during  interaction.  As  your  self 
develops  into  a  fuller  individuality,  a  greater  world  of 
spiritual  content,  your  resultant  acts  partake  of  a  larger  and 
more  significant  freedom.  It  may  now  be  maintained  that 
our  arguments  have  led  us  back  to  determinism,  for  have 
we  not  admitted  that  the  agent's  act  is  a  mere  result  of  his 
soul  content  at  the  given  time?  The  agent  could  not  have 
acted  in  a  different  manner,  and  consequently  the  inference 
is  that  the  agent  is  absolutely  determined.  We  grant  this 
without  hesitation  because  this  is  what  we  mean  by  a 
rational  freedom,  but  we  do  not  grant  that  the  act  was 
determined  for  the  agent,  but  by  the  free  choice  of  his  own 
individuality  or  self.  Genuine  freedom  is  a  measure  of  the 
magnitude  of  the  individuality;  it  does  not  measure  the 
magnitude  of  some  other  alien  self.  Our  freedom  is  in  the 
nature  of  a  creative  determinateness  and  not  an  external 
absoluteness  or  manifestation  of  chaotic  chance.  The  crea- 
tive work  of  art  finds  its  expression  in  and  through  a  me- 
chanical system.  The  physical  world  and  nature  consti- 
tute the  instrument  of  expression  of  spiritual  values.  Mind 
is  not  a  compound  formed  by  association  of  a  number  of 
unrelated  and  separate  content  units.  It  is  rather  a  growth 
by  differentiation  from  a  unity  which  pervades  the  con- 
scious being  and  the  physical  universe.  We  hold,  there- 
fore, that  the  unitary  being  of  the  soul  is  free  in  its  activity 


SCIENTIFIC  THEISM  205 

expressions,  that  its  activity  expressions  are  genuine  self- 
expressions  and  not  expressions  of  some  external  agent, 
and  that  the  manner  of  the  activity  expressions  is  influ- 
enced and  partially  controlled  by  the  necessities  imposed 
by  environment. 

124.     The  Assurance  of  Immortality. 

The  finite  self  longs  for  the  transformation  of  the  dis- 
cords of  life  into  harmonious  forms.  This  is  the  main- 
spring of  life  and  the  root  of  hope.  The  path  of  discord 
leads  the  finite  self  out  of  itself  and  beyond  itself  in  the  con- 
templation of  a  condition  of  existence  in  which  its  loftiest 
desires  may  find  their  completion.  In  the  final  analysis  we 
desire  that  the  best  in  us  shall  persist.  The  best  in  us  in- 
cludes what  is  beyond  us.  The  finite  self  seeks  its  fuller 
expression  in  a  perfection  which  cannot  be  realized  during 
finite  life.  Souls  are  hurled,  as  it  were,  from  the  Heart  of 
the  Infinite  into  the  temporal  world  of  discord  and  experi- 
ence, where  they  are  moulded  into  self-conscious  beings  of 
thinking  wills  seeking  perfection  because  aware  of  imper- 
fection, and  living  in  hope  of  an  ultimate  return  to  a  timeless 
world  of  perfection  and  harmony.  The  universality  of  this 
hope  is  the  greatest  natural  law  in  the  universe.  It  is  the 
source  of  that  feeling  of  certainty  that  our  finite  self  will  not 
be  denied  the  realization  of  its  desire  for  a  fuller  expression 
in  a  life  beyond  this.  If  this  feeling  is  mere  superstition, 
then  the  world  becomes  meaningless.  The  universal  belief 
in  immortality  cannot  be  a  mere  development  from  experi- 
ence and  environment.  Even  the  most  primitive  of  the  an- 
cient races  of  mankind  held  the  belief  in  immortality  in 
some  form.  This  belief  could  not  have  arisen  in  the  primi- 
tive mind  from  experience  and  environment.  Physical  evi- 
dence showed  primitive  man  nothing  but  an  absolute  end 
with  the  death  of  the  body.  Therefore  we  maintain  that  the 
belief  in  immortality  is  more  than  belief:  it  is  a  universal 
factor  in  the  subconscious  content  of  the  conscious  self.  No 
matter  how  subtle  the  attempt  may  be  to  derive  the  belief 
from  experience,  the  universal  evidence  of  bodily  death  con- 
stitutes a  universally  true  fact  out  of  which  a  normal  mind 
can  derive  nothing  but  an  absolute  negation  of  immortality. 
Despite  this  observation,  the  fact  of  bodily  death  has  em- 
phasized the  belief  in  immortality.  Therefore  the  normal 


206  SCIENTIFIC  THEISM 

mind  is  either  universally  inconsistent  and  incapable  of 
deriving  correct  inferences  from  facts,  or  the  belief  in  im- 
mortality is  grounded  in  the  depths  of  reality  and  is  known 
as  an  eternal  verity  to  the  subconscious  phase  of  soul  life. 
We  hold  that  the  subconscious  world  is  nearer  the  Gates  of 
Paradise  than  the  intellectual  world  built  upon  a  substruc- 
ture of  logical  inference.  We  maintain  that  the  revelations 
which  reach  the  conscious  world  via  the  subconscious  are 
truer  glimpses  of  the  Life  Eternal  than  the  manufactured 
products  of  the  logical  laboratories.  Hence  we  regard  the 
assurance  of  immortality  as  a  God-given  endowment  to  the 
subconscious  phase  of  soul  life.  This  eternal  verity,  known 
as  such  to  subconsciousness,  therefore  appears  in  conscious- 
ness as  a  persistent  and  necessary  intuitional  truth  which 
finds  no  definite  point  of  entry  in  the  scheme  of  logic.  Im- 
mortality finds  its  place  as  the  complement  of  the  intent  of 
reality.  Logic  and  reason  cannot  determine  the  type  or 
form  which  this  fuller  experience  will  assume  beyond  death. 
The  link  of  personal  recollections  is  not  shattered  by  death. 
In  the  fuller  life  our  demand  for  a  growing  and  higher  ex- 
perience will  find  its  satisfaction. 

CONCLUDING  REMARKS 

Looking  in  retrospect  upon  the  matter  presented  in  this 
work,  we  fully  realize  that  a  mere  suggestive  outline  of 
possibilities  has  been  presented.  It  is  our  hope  that  suffi- 
cient possibilities  have  been  outlined  to  interest  others  in 
the  further  development  of  this  spiritual  concept  of  the 
physical  universe. 

We  have  found  that  the  Spirit  of  God  manifests  in  the 
microcosm  and  in  the  macrocosm,  in  the  unconscious  as  well 
as  in  the  subconscious  and  conscious,  in  the  monon  and 
viton  as  well  as  in  the  most  complex  form  of  mental  life. 
The  world  is  a  created  revelation  of  a  Timeless  Reality  in 
temporal  finiteness.  The  intent  of  this  Timeless  Reality 
deferred  in  time  leaves  the  imprint  of  purpose  and  teleology 
throughout  the  universe.  The  temporal  desire  for  harmony 
with  the  Timeless  Reality  is  a  world  teleology  which  points 
toward  Absolute  Truth,  Absolute  Freedom,  and  the  Har- 
mony of  Finite  Being  with  the  Life  of  God. 


APPENDIX  A 

A  NON-NEWTONIAN  DEVELOPMENT  OF  THE  PLANETARY 

ORBITS 

125.  The  Planetary  Orbits  According  to  the  Space-Time  Po- 
tential. 

In  our  development  of  the  planetary  orbits  we  shall 
make  use  of  no  other  relations  than  those  set  forth  in  statics 
and  dynamics.  Moreover,  we  shall  make  no  use  of  the  New- 
tonian inverse  square  hypothesis.  The  central  force  notion 
of  Newton  we  shall  abandon  for  an  assumption  which  con- 
tains within  itself  a  sufficient  physical  reason  for  an  orbit  of 
unequal  axes.  A  single  constant  central  force  contains 
within  itself  no  physical  reason  to  account  for  such  a  modi- 
fication of  a  circular  orbit.  In  the  plane  of  the  orbit  we 
shall  introduce  two  unequal  force  factors  acting  in  a  two- 
directional  manner.  Moreover,  we  shall  assume  that  space 
is  a  sense  chart  of  position  values  in  such  a  manner  that 
the  location  of  a  thing  in  space  is  determined  by  the  direc- 
tional intensity  of  the  interaction  at  the  particular  position. 
Furthermore,  we  shall  suppose  that  space  is  not  an  obstacle 
to  interaction,  but  a  measure  of  the  relative  intensity.  These 
are  the  basic  suppositions  of  our  Space-Time  Potential  in 
accordance  with  which  we  shall  now  investigate  the  orbital 
motion  of  a  body  in  a  plane  of  space. 

Let  the  components  of  the  activity  intensities  in  any 
given  plane  AA  of  space,  chosen,  for  the  sake  of  convenience, 
at  right  angles  to  each  other,  be  of  equal  magnitude,  then 
the  intensity  of  the  action  or  stress  upon  any  plane  BB 
perpendicular  to  the  given  plane  AA  and  making  any  angle 
whatsoever  with  the  direction  of  the  components,  will  be 
of  equal  magnitude.  In  other  words,  the  resultant  of  the 
tangential  and  normal  stresses  on  the  plane  BB  will  be  equal 
to  the  resultant  of  these  stresses  if  plane  BB  is  revolved 
into  any  other  position  CC. 

A  body  free  to  move  in  a  plane  AA  subjected  to  such 
activity  conditions  will  move  in  a  circular  orbit  and  will  be 

207 


208  SCIENTIFIC  THEISM 

in  dynamic  equilibrium  in  this  orbit.  The  radius  r  of  this 
orbit  will  remain  a  constant  equal  to  the  initial  radius  ob- 
served for  the  given  body  assumed  to  move  in  the  plane  AA. 

If  the  observed'  orbit  is  not  circular,  then  the  stress  com- 
ponents are  unequal  in  magnitude. 

If  the  stress  components  are  unequal,  then  the  orbit  of 
the  body  is  a  conic  section.  The  type  of  the  conic  depends 
upon  the  relative  magnitude  of  the  stress  intensities. 

We  shall  now  investigate  the  activity  conditions  prevail- 
ing in  a  plane  subjected  to  a  two-directional  stress  system  of 
unequal  intensities. 

For  purposes  of  analysis  let  us  take  any  plane  AAAtAv 
in  space  (see  Fig.  16) .  The  resultants  of  the  activity  fact- 
ors outside  of  the  limiting  boundary  of  this  particular  space 
AAAiAi  may  be  reduced  to  the  intensity  factors  Fy,  Fy, 
equal  in  magnitude  but  opposite  in  direction ;  and  Fx,  Fx, 
also  equal  in  magnitude  and  acting  in  opposite  directions. 
As  far  as  the  plane  AAA1A1  is  concerned,  the  external  activ- 
ity factors  are  in  equilibrium.  This  assumption  is  therefore 
in  complete  accord  with  the  general  procedure  in  dynamics 
as  well  as  in  statics.  The  general  case  of  the  above  is  when 
Fv  is  not  equal  to  Fx. 

In  Fig.  17  we  have  resolved  the  intensity  factor  Fv  into 
a  tangential  component  Tv  and  a  normal  component  Nv  with 
reference  to  the  plane  BB. 


In  the  triangle  PQR  we  have 
Similarly, 


•    „    Nv 
sin  &  =  ^r-     and 


T 

cos  £  =  -=r     and    Ty  =  Fy .  cos  fi. 

*y 
Since  the  axis  XX  is  perpendicular  to  the  direction  of  Fv, 

it  follows  that  a  unit  area  along  XX  corresponds  to  an  area 
along  BB  found  from  the  following  relation : 

A  A 

sin  0  =  -T-2,     hence     AB  =  -r-^  • 
AB  sin  $ 

Now  since  Ax  =  1,  it  follows  that  the  corresponding  area 
along  BB  is  given  by 


SCIENTIFIC  THEISM  209 

If  /  =  intensity  of  the  action  per  unit  of  area  upon  any 
plane  BB  and  /  =  the  magnitude  of  this  action  upon  an 
area  AB,  it  follows  that 


Hence  it  is  clear  that  the  unit  area  intensity  of  the  normal 
component  N,,  along  BB  is  expressed  by 

XT      Fy .  sin  B      , 

Ny  =    *    . — * ;    because    AB  =  1  -s-  sin  B. 

Consequently, 

Ny  =  Fy.sinf  6. 

Similarly,  we  have  for  the  unit  area  intensity  of  the  tangen- 
tial component  Tv  along  BB, 

T»-i*iS!"F*-€oi  Min  p- 

Referring  to  Figures  17  and  18,  we  find  that  N,  and  N,  act 
in  the  same  direction,  while  Tv  and  Tx  act  in  opposite  direc- 
tions. If  we  regard  the  components  of  Fv  as  positive,  then 
Nf  is  positive  and  Tx  is  negative. 

Considering  a  unit  area  along  YY,  we  have  in  the  same 
manner  as  above, 

-B)=Az  A_         Ay 
p'     AB'  sin  (90°-p) 

1  1 


£)     cosp 
Moreover,  from  triangle  PLM  we  find 

and    Nx 


Furthermore,  we  obtain  the  relation 

—  T 

sin  $  =  -^rJ~    and 

*x 

For  unit  area  intensities  we  have 


—  T 

sin  $  =  -^rJ~    and     Tx=— 


The  negative  sign  has  been  introduced  here  since  Tx  acts  in  a 
direction  opposite  to   Tv.     Combining  similar  components  of 
Fv  and  Fx,  we  obtain 
N  (the  total  normal  component)  =  Ny+Nx, 

=  Fy.sin* 


210  SCIENTIFIC  THEISM 

T  (the  total  tangential  component) 

=  Ty+Tx 

=  Fy.cos  p.  sin  ft  —  Fx.sin  ft.  cos  ft, 

-sin  p.  cos  ft(Fy-Fx). 

In  Fig.  19  the  resultant  R  of  N  and  T  is  given  by  the  line  PV. 
It  is  evident  that 

R-V/N'+T1. 

Substituting  the  values  of  N  and  T  in  this  equation,  we  have 
R=V{Fy.sin2ft+Fx.  cos2  ft}2+  {sing,  cos  ft(Fy-Fx)}2 
=V{Fy.sin2ft+Fx.cos2ft}2-Hsin2ft.cos2ft(Fy-Fx)2 

R  =VFy2  {  sin4  0+sin2  0  .  cos1  0  }  +FX2  {  cos4  ft  +sin  2ft  .  cos2  ft  } 


-f  2Fy.Fx  {sin2  ft.  cos2  ft  -sin2  ft.  cos2  ft. 
Since    {  sin2  ft.  cos2  ft—  sin2  ft.  cos2  ft}  =0,    the  expression  becomes 


The  value  (sin*{i-f-  cos*^)  =  l,  consequently  the  last  expression 
reduces  to 

R  =VFy2.sin2£+Fx*.cos2p.          (In  Fig.  19,  R  =  P  V.) 
The  resultant  R  makes  the  angle  9  with  the  plane  BB. 
This  is  evident  from  Fig.  19,  from  which  we  see  that 

tan  9  =  £  «BPV  =  <PVW  =  9). 

By  substituting  the  values  of  N  and  T  in  this  equation  we  have 

^Fy.si 
a<p~sm£. 

If  we   divide   both    numerator  and   denominator  of  this   last 
expression  by  cos2  @,  we  obtain 

Fy.sin2  fi    Fx.cos2  ft 
cos2  ft          cos2  ft         Fy.tan2 

_ 
y       x 


In  Fig.  19,  let  6  =  angle  between  PV  (i.  e.  fl)  and  PZ  (the 
direction  of  Fy).     The  following  relation  holds  good: 

l-(fl-t) 
Consequently, 

tan     —  tan    9 


SCIENTIFIC  THEISM  211 

If  we  substitute  the  value  of  tan  <p  obtained  above  in  this  last 
expression  we  have 


tan  o  =  • 


tan  0  [(Fy-Fx)  +  {Fy.tan2  0+Fx}] 

-tan2ft.Fx-FK  -F^l+tan2  g) 

tan  £  .  Fy+tan  £(Fy  .  tan2  £)  tan  £  .  Fy(l+tan2  £ 

Hence. 

F  F 

tan  6=-p  **     Q=-rr.cot  p. 
Fy.tan  £        Fy 

Let  j/  =  Fy.sin  £  and  a^F^.cos  /?;  then,  since 
R=VFy2.sin2 


This  equation,  being  of  the  second  degree,  is  a  conic  section. 

Let  the  coordinates  of  any  point  D  on  this  curve  (see 
Fig.  20)  be  x,  y.  To  construct  the  conic,  proceed  as  follows  : 
With  point  P  as  a  center,  describe  the  outer  circle  with  a 
radius  F9.  Similarly,  draw  the  inner  circle  with  a  radius 
Ft,  since  Fv  has  been  assumed  greater  than  Fx. 

Any  point  D  on  the  curve  of  the  conic  must  satisfy  the 
relation  /?  =  j/8  -\-  x\ 

Take        P#  =  x  =  Fz.cos  p     and 


where  angle  /3  is  the  angle  which  the  plane  BB  makes  with 
the  Y  axis. 

These  values  of  x  and  y  determine  any  point  D  of  the 
curve. 

We  may  locate  any  point  D  of  the  curve  by  the  following 
method  :  In  Fig.  20,  PC  is  constructed  perpendicular  to  the 
plane  BB.  From  the  point  C  where  PC  intersects  the  outer 
circle,  line  CE  is  constructed  perpendicular  to  the  Y  axis 
and  consequently  parallel  to  the  X  axis.  From  the  point  of 
intersection  G  of  PC  and  the  inner  circle,  line  FG  is  drawn 
parallel  to  the  X  axis.  Also  from  point  G,  line  GD  is  made 
parallel  to  the  Y  axis.  The  intersection  of  lines  GD  and  CE 
determines  the  point  D  in  the  curve.  Moreover,  the  line  PD, 


212  SCIENTIFIC  THEISM 

connecting  points  P  and  D,  is  the  radius  vector  of  the  curve, 
and  it  is  commensurate  with  R,  the  resultant  stress  upon  the 
plane  BB.  Furthermore,  the  direction  of  line  PD  repre- 
sents the  inclination  of  the  resultant  stress  to  the  plane  BB. 
That  this  construction  satisfies  the  relations 

y  =  Fy.sin  £,  and  x»F,.cos  $ 

will  now  be  shown. 

In  Fig.  20,  the  construction  is  such  that 

PC=  Fy;  PG  -  Fx;  PE  =  y;  and  FG  =  ED  =  x. 
Moreover,  the  following  relations  are  true  : 
angle  CPE  =  (90°  —  /3),  and 

PE 

cos(90°-&)=~;   PE  =  PC{cos(90°-0)}-Fy.sin  0-y; 
"\j 

FG 
sin(90°-B)  =  pg;   FG«PG{sin(90°-p)}  =-F,.cos  p-x. 

It  is  evident  that 

PD'-PE'+ED*,  and,  consequently, 
R»=.y»+x1  =  Fy».sma  £+  F,8.cosa  p. 
Furthermore, 

*-  T^W    ED     F,.cos  fi     F, 
Un  <  DPE-Fg-f^ir|  =  F;.cot  p. 

We  have  seen  that 

F 
—  pr.cot  0=»tan  6,  therefore 

tan<DPE  =  tanO,  and  <DPE  =  <6. 
In  Fig.  20  the  resultant  PD  =  R  is  in  the  first  quadrant,  and 
the  inclination  angle  $   which  it  makes  with  the  plane  BB  is 
therefore  greater  than  angle  £,  consequently, 
9  =  6-f-{i    and     6  =  (<p  —  (i). 

Hence  tan  6=  tan  (<p  —  (i).     By  proceeding  as  above  we 
find  that 


which  is  the  same  value  as  obtained  for  tan  (£  —  ?)  with  the 
opposite  algebraic  sign. 
Hence 

F 

tan  6-+=r.cot  &• 
*y 

Consequently,  the  construction  satisfies  the  necessary  conditions 
imposed  by  the  fundamental  relations  previously  developed. 


SCIENTIFIC  THEISM  213 

We  shall  now  prove  that  the  extremity  of  the  radius  vector 
R  traces  a  conic.     Referring  again  to  Fig.  20,  we  find  that 
PV==PG_2=FG2=DE2=_x-)  Bince  FG^DE. 
Fy2~PC2    CE2~CE2    CE2' 
but    CE2=LE(KE);    therefore 
JV  x' 

Fy2  =  LE(KE)* 

Since  KE-(Fr—y)  and  L#=(Fy+y),  it  follows  that 
F,2  x2  x2 

FyjaBS(Fy4-y)  (Fy-y)  =  (Fy2-y2)' 
which  gives 

Fx2(Fy2-y»)-FyVx2,  or 


which  is  the  equation  of  a  conic. 

If  the  terms  of  this  expression  be  divided  by  Fs*.Fy*,  we 
obtain  the  equation  in  its  most  easily  recognized  form  as  follows: 

x9      v1 

— —  -L  *  .  =«1 

F,2^Fy» 

In  this  form  we  readily  recognize  the  conic  as  an  ellipse. 
It  is  apparent  that  the  type  of  the  conic  depends  upon  the 
relative  magnitude  of  the  activity  factors  Ff  and  Fv.  If 
these  factors  are  equal  to  each  other,  the  conic  becomes  a 
circle.  If  they  are  unequal  in  magnitude,  the  curve  is  an 
ellipse  which  tends  toward  a  parabola  when  the  ratio  of 
their  intensities  approaches  an  infinite  value.  Conversely, 
if  the  orbit  is  an  ellipse,  the  activity  factors  prevailing  in 
the  plane  of  the  orbit  are  unequal  in  their  magnitude.  For 
negative  values  of  FJ  the  curve  becomes  an  hyperbola. 

An  exhaustive  investigation  of  a  material  system  inter- 
acting according  to  the  Space-Time  Potential  involves  a 
reference  to  a  three-directional  system  of  coordinate  axes. 
The  space  of  sense  is  most  conveniently  regarded  as  a  triply 
extended  manifold.  The  Newtonian  hypothesis  is  primarily 
a  one-directional  vectorial  system  regarding  the  sun  as  a 
central  force.  The  one-directional  attraction  between  the 
sun  and  the  earth  is,  according  to  Newton,  a  sufficient  reason 
for  the  earth's  orbit  type.  We  cannot  agree  with  this  con- 
venient simplification,  for  the  reason  that  any  finite  portion 
of  a  plane  in  space  must  be  under  the  influence  of  a  two- 
directional  activity  system.  In  this  manner  only  are  we  able 


214  SCIENTIFIC  THEISM 

to  include  all  the  activity  factors  within  the  plane  beyond 
the  confines  of  the  finite  portion  considered.  By  referring 
the  finite  portion  to  an  X  and  a  Y  axis  all  activity  factors 
in  the  plane  will  be  either  above  or  below  the  X  axis  and  to 
the  left  or  the  right  of  the  Y  axis. 

We  conclude,  from  the  above  mathematical  analysis, 
that  a  body  free  to  move  under  the  action  of  the  unequal 
forces  Fv  and  Fa  in  the  plane  AAA1A1  will  describe  a  locus 
consistent  with  the  requirements  that  the  resultant  R  of  the 
unequal  activity  factors  shall,  for  all  points  of  the  locus, 
satisfy  the  relation 


R=\/FyJ.sin2 

That  the  locus  is  a  conic  section  has  already  been  shown. 

We  shall  now  supplement  the  above  statical  analysis  by 
two  additional  proofs  based  upon  the  laws  of  dynamics.  It 
is  to  be  noted  that  the  Newtonian  inverse  square  hypothesis 
has  been  discarded. 

126.    The  Keplerian  Relations  according  to  the  Space-Time 
Potential. 

Let  us  now  consider  the  problem  from  another  stand- 
point. In  Fig.  21,  let  the  radius  PR  of  the  inner  circle  RG^A 
be  commensurate  with  a  force  Fx,  and  let  the  radius  PK  of 
the  outer  circle  KCJ$  be  commensurate  with  a  force  F,.  The 
distance  RK  is  then  commensurate  with  (Fv  —  F»).  Let 
point  N  be  the  mid-point  of  the  distance  RK  and  let 
e  =  RN  —  NK.  The  circle  NNtN2  passing  through  point  N 
and  having  P  as  its  center  is  then  the  mid-locus  of  the  ring 
area  KBAR.  The  length  RN  =  NK  =  e.  is  therefore  com- 
mensurate with  (Fv  —  Fx)  -=-2,  and  the  locus  NNtNt  may 
be  regarded  as  a  neutral  locus.  In  order  that  the  action 
which  we  are  about  to  investigate  may  be  easily  understood 
we  shall  imagine  that  the  body  is  connected  to  the  origin  P 
by  a  resistive  spiral  spring.  At  first  we  shall  confine  the 
direction  of  the  motion  of  the  body  to  the  line  RK.  More- 
over, we  shall  assume  that  initially  the  body  is  located  at  the 
mid-point  N  in  the  neutral  locus  NNiN2.  The  movable  body 
may  then  be  displaced  through  the  distance  NK  whenever 
it  comes  under  the  periodic  influence  of  the  outward  acting 
force  —  (Fv  —  F*)  •+•  2.  We  use  the  negative  sign  in  con- 


SCIENTIFIC  THEISM  215 

nection  with  this  outward  force  in  order  to  distinguish  the 
direction  from  the  +  (F,  —  Fm)  -±-  2,  which  we  consider 
as  being  directed  toward  the  origin  P.  The  periodic  dis- 
placement of  the  body  through  NK  against  the  inward  re- 
sistive force  -f  (Fv  —  Ff)  -=-  2  is  much  the  same  as  if  the 
body  were  periodically  seized  by  an  external  agent  and 
dragged  through  this  distance  against  the  resistive  force  of 
a  spring.  The  path  RK  may  be  regarded  as  a  smooth,  fric- 
tionless  slide  or  plane  surface  upon  which  the  body  can 
oscillate.  Our  preliminary  investigation  will  confine  the 
body  to  an  oscillatory  motion  along  this  slide. 

Let  the  force  required  to  displace  the  body  a  unit  dis- 
tance along  the  vector  against  the  resistive  force 
+  (^*  —  ^«)  -j-  2,  regarded  as  acting  toward  P,  be  repre- 

sented by  f.     The  total  force  Fe  necessary  to  displace  the 

body  through  the  distance  NK  =  e  is  then  f  e  =  Fe. 
Suppose,  now,  that  the  body  has  been  brought  to  the  point  K 
by  the  action  of  the  outward  force  —  (F,  —  Fg)  -r-  2  =  Fe. 
Upon  the  cessation  of  the  activity  of  Fe,  which  we  can 
properly  assume  at  this  stage  of  the  analysis,  the  body 
begins  its  return  motion  in  a  direction  toward  point  P. 
When  it  has  moved  through  a  distance  i  =  KM  it  has  arrived 
at  any  general  point  M. 

At  the  point  M  the  available  force  F  z  is  commensurate 
with  the  remaining  distance  to  N;  that  is,  the  distance 
MN  =  (e  —  i)  =  z.  Hence 

F-  =/»  =/(-0- 

If  for  the  body  at  any  general  point  M  we  let 
v  —  velocity, 
a  =  acceleration,  and 
m  =  the  mass  then 

di  dv  ,. 

t>  =  -rr»     a  =  "rr»     and     vdv  =  adi 
dt'  dt 

At  the  point  M  the  available  force   F,=/(e—  i)«=m.a 
and  , 


m 
Substituting  this  value  of  o  in  v  dv  =  a  di,  we  have 

,      /(e-i)    .. 
v  dv  =  -  -  '-  .  di 
m 


216  SCIENTIFIC  THEISM 

Integrating  from  o  to  v  and  from  o  to  i,  we  obtain 


fT  A        //(e-i) 
I  vdv=»  I  -  -  -.di, 

•'• 


-(e-i).di-(e.di-i.  di) 

^_/Jei_i'C    and  v^/Li    i' 

2      m(        2)'  m|        2J     m 


which  gives 


An  inspection  of  this  last  equation  reveals  the  fact  that 
»=»o  when  i=o,  or  when  i—2e;  consequently  the  body  will 
oscillate  between  the  points  K  and  R. 

When  i  =  «,  v  has  a  maximum  value  given  by 


m 

Since  V--T-,  dt=>~,  and  therefore 
at  v 


where  <  is  the  time  required  for  the  body  to  traverse  the  distance 
fe. 

Now,       I      .     .      .  »arc  ver  sin  (-  J. 
yV2ei-i*  \e/ 


If  in  Fig.  21  the  circle  KHR  be  described  with  NK  as  a 
radius,  then  in  the  triangle  NMH  we  have 

(NH-MN) 

ver  sin   8=»1—  cos   8-=-^  -  ^^  -  -: 

NH 

but 

(NH-MN)  «(NK-NM)-(e-i)-e-(e-i)-i. 

Therefore,     ver  sin  8=-,     and  it  follows  that  9  is  the  arc 
e 

whose  ver  sin  =  -.     It  is  also  evident  that 
e 

//m  i]*» 

dt  =  A/  J.arc  ver  sin  - 


SCIENTIFIC  THEISM  217 

The  motion  of  the  body  from  point  K  =  o  to  point  R 
over  the  path  KR  =  2e  corresponds  to  a  variation  of  the 
angle  6  from  0°  to  180°.  In  circular  measure,  since  the 
radians  in  1°  =  n  -=-  180° ;  we  have  d  =  n,  when  #  is 
measured  in  degrees  =  180°.  These  values  correspond  to  a 
value  of  t  =  2e.  From  these  observations  the  following  re- 
lation should  be  self-evident: 


It  is  seen  that  in  the  circle  KHR  the  ordinate  drawn 
from  any  position  M  of  the  body  moving  in  the  path  of  KR 
intercepts  an  arc  KH  which  determines  the  instantaneous 
value  of  <5. 

The  general  expression  (circular  measure)  for  t,  the 
time,  is  therefore 


In 

\r 


t-8 

Investigating  the  dynamic  relations  pertaining  to  the 
moving  point  M  in  the  rectilinear  path  KR  and  the  point  H 
in  the  circular  path  KHR,  we  find,  for  the  point  M  moving  in 
KR,  the  following  expression  for  velocity,  acceleration,  time, 
etc.,  corresponding  to  simultaneous  positions  of  H ; 

1.  versin  3  =  (l-cos  &)  =  !-(— \  =  ! 

2.  i-se.ver  sin  S—eCl— cos  8) 

3.  t 

Since  di  =  d{e(l— cos  8)=e.sin  S.d(S),  and 
-ei  (8); 


then,  if  we  substitute  these  values  in  the  general  expression 

di 

V=-TT>  we  have 
at 

di     e.sin  S.d(8)        fT 
4.        T=^=    . —  =A|r-.esin8 

_Vr 

c  J  \    ~      )       J 

m     ~m 


218  SCIENTIFIC  THEISM 

This  is  evident  because  (e  —  i)=e(cos  8). 

From  Equation  3  we  have  t  =  8.»l-T,  consequently 


and 
6. 


7.         —  TJ—  =  *l  —  =  angular  velocity  =  ji. 


In  Fig.  21  z  =  (e—  0=JV~-^  =  e.cos  8,  hence  the    following: 

8.  dz=—  e.sin  S.d(8). 

9.  d2z=-e.cos  8(d8)8=-z.(d8)J; 
but  since 

(x.dt,  and 


d2z=-z.((j..dt)J, 
hence 


From  Equation  7  we  observe  that  p  the  angular  velocity 
is  constant.  In  other  words,  the  rate  of  increase  of  8  is 
uniform,  and  the  point  H  travels  in  its  circular  orbit  KHR 
about  point  N  as  a  center  at  a  uniform  rate. 

Equation  10  may  be  developed  as  follows,  using  point  N 
as  the  origin : 

Let  arc  KH  =  h,  then  in  circular   measure    8  =  -. 

e 

When  the  body  is  at  K  the  time  is  represented  by  £0,  and 
when  it  is  at  any  point  H  in  the  circular  orbit,  the  time  is  t; 
hence  the  time  required  in  the  passage  from  K  to  H  is 
(t  —  £0).  Knowing  from  the  above  discussion  that  v  is 
constant,  we  have 

v=  .,     and     h  =  v(t— 10). 

From  the  figure  we  see  that 

z  =  e.cos  S=e.cos(  -  )  =  e.cos<-(t— 10)>, 
\e/  \ev 

=  e.cos<-.t — .' 


SCIENTIFIC  THEISM  219 

Since  ,/h\     1  ,,  .v 

J/*A     dl  -  1     -d(vt) 
d(5)       Ve/     e    v    '     v,  .. 

1*  =  —  rr  =    V     =  —  TT  —  =  -(a  constant); 
dt         dt  dt        e 

therefore  we  have  by  letting 

V=-|.t0=-(A.to, 

c 

11.  z  =  e.cos{{i.t—  [i.t0}  =  e  .  cos  {  (x(t  —  10)} 

=  e.cos{(jt.t+v}. 
The  velocity  v,  of  the  body  along  the  rectilinear  path  KR  is 

expressed  by  V»  =  T 

dt 

_  dz  _  d[e.cos{(jLt+v|]  _  — 
V'~dt~         "~dT~  ~~dt 

but  since,  d{(it+v}  =(i.dt,  it  follows  that 

,0  —  e.sin{(xt+v}(i.dt 

12.  v,  =  -  L!    -  —  —  =~ 


Let  a  =  the  acceleration  of  M  along  KR,  then 

d2z 

13.  a  =  -7r^=—  e.[i2.cos{(it+v},  and  since 

z  =  e  .  cos  {  (it  +  v  }  ,  by  substitution  we  obtain 

H27  H27 

14.  a  =  ^=-^.Z,  or  ^'..-O. 

This  equation  is  identical  with  Equation    10. 
Dividing  both  members  of  Equation  14  by  z,  we  have 

o  fl        7 

15.  -  =  —  i—  —  =  —  u.2  (a  negative  constant). 
z  z 

By  using  the  transformation  formula 

cos(a+b)=cos  a.  cos  b  —  sin  a.  sin  b  in 
Equation  11,  we  obtain 

16.  z  =  e.cos{|it+v}  =e[cos  (it.  cos  v—  sin  (xt.sin  v]; 
and  letting 

T=  —  e.sin  v,  and  U  =  +e.cos  v, 

we  can  reduce  Equation  16  to  the  general  form  for  simple  har- 
monic  motion,   viz.; 

17.  z  =  T.sin  (xt+U.cos  {xt  =  e.cos{[xt+  v}. 

If  p  is  the  period  of  one  complete  oscillation  =2(KR)  and 
corresponding  to  a  value  of    8  =  360°  =  2z   (circular  measure) 

we  have,  since  fnT 

t=  8-1-7-         (see  Equation  3), 

2x      2ic  \T 

t  =  -J==~  for  by  Equation  7,  n  =  ^|  ^ 

\m 


220  SCIENTIFIC  THEISM 

Moreover,  in  the  above  expression  e  is  the  amplitude,  and  since 


the  phase 

*°~~H 

The  law  expressed  by  Equation  10  is  equally  the  law  of 
electric  oscillations  if  the  resistance  is  neglected.  If  we  let  v 
be  the  electromotive  force  of  the  system,  measured  in  volts, 
we  have 

d2v  ,  n      u 

:rn-r(A  -v  =  0,  where  (i  is  a  constant. 

ThUs  far  we  have  investigated  the  dynamics  of  the  body 
for  a  motion  confined  to  the  rectilinear  path  KR.  We  have 
seen  that  if  the  motion  of  the  body  be  defined  by  the  motion 
of  H  in  the  circular  orbit  KHR,  then  H  will  describe  equal 
arcs  in  equal  time,  and  the  angular  velocity  of  the  vector  NH 
will  be  constant.  We  shall  now  make  the  further  assump- 
tion that  the  vector  KRP  rotates  about  P  as  a  center,  and 
that  simultaneously  with  this  motion  the  body  moves  with 
a  constant  angular  velocity  //  about  the  origin  N  as  a  center. 
At  the  end  of  a  definite  interval  of  time  tt  the  vector  is  in 
the  position  PGiCi.  We  shall,  moreover,  consider  that  the 
path  or  orbit  of  the  body  is  at  all  times  controlled  by  two 
forces,  one  parallel  to  the  X  axis  and  the  other  parallel  to  the 
Y  axis.  Furthermore,  we  shall  investigate  the  case  in 
which  these  forces,  acting  in  normal  directions  to  each 
other,  have  for  their  resultant  a  constant  magnitude  = 

2(Fy~Fl)=2(NK)  =  KR  =  (Fy-F,). 

The  motion  of  the  body  is,  therefore,  confined  to  the  ring 
area  RKBA. 

In  triangle  GidDt  (Fig.  21)  the  following  relation  is 
evident :  TT^n 


Let  us  designate  the  involved  magnitudes  as  follows: 
/»  =  force  parallel  to  the  X-axis. 
/„= force  parallel  to  the  F-axis, 
F  —  (Fy  —  Fx)  =  resultant  =  a  constant. 

We  may  then  write  for  any  position  of  the  vector  PK, 


At  any  point  Dt  the  forces  /*  and  /„  may  be  resolved  nor- 
mally and  tangentially  to  the  direction  of  motion.    It  is  evi- 


SCIENTIFIC  THEISM  221 

dent  that  if  this  is  done  the  sum  of  the  squares  of  these  force 
components  must  equal  (fx)s+(fy)l=F1=  a  constant. 
In  the  triangle  GidDi  we  have 

Fy.cos  pi-Fx.cos  pi=»(Fy-Fx)cos  0lf  and 
T.sin    £i-Fx.sin    fr  =  (Fy  -  Fx)sin    fr. 


But  since  DjGj  -fCJDcsCGssF   we  have 
F2  =  (Fy-Fx)».sin'  fc+(Fy-F,)«.coB«  0i; 
therefore 

F'=(Fy-Fi)«, 

which  is  identical  with  our  original  assumptions,  and  it  follows 
that  the  coordinates  of  point  Dt,  with  P  as  the  origin,  are 
x  =  MDi  =  Fx.cos  PI  and 
y  =  DiJ  =  Fy.sin  fr. 

Consequently  the  locus  of  points  satisfying  the  condition 
Fl=(fx)2-f-(fy)1  =  a  constant  and  described  as  shown  is  a  conic. 
This  should  be  evident  from  the  previous  developments. 

In  Fig.  21  it  is  evident  that  as  the  vector  rotates  <£oCi 
of  any  triangle  G1C1D1=  ^KPC:=  the  vectorial  angle. 
Moreover,  <$oCi  =  <^DiGriCi  is  measured  by  one  half  arc  CJ)lf 
and  the  central  angle  DjnCj  is  measured  by  arc  CiDt. 
Consequently  <£  DinCi  =  2oCi=5i.     By  Equation  7  we  know 
that   our   primary   suppositions   gave    us   a   constant   angular 
velocity  for  the  body  actuated  by  the  assumed  force  factors. 

In  other  words,      ,     **  a  constant,  being  a  consequence  of  the 

force  activities  assumed  primarily;  therefore,  the  continuity 
of  this  condition,  taken  in  conjunction  with  the  rotation  of  the 
vector,  means  that  the  sub-vector  Dtn  will  describe  equal 
arcs  in  equal  times,  and  the  rate  of  increase  of 

2oCi=8i  is  uniform. 

From  this  fact  we  conclude  that  since 

d(S)=d{2(oQ}  , 

-rr-       '   \        =a  constant,  therefore 
at  at 

d(&)     also  is  a  constant,  which  means  that  if  F1 
"IT 

shall  equal  \j       +  J    \  =  a  constant,  the  angular  velocity 

of  the  vector  PCt  must  also  be  constant,  because  to  satisfy 
this  condition  the  principal  vector  PC,  must  always  describe 
the  angle 


222  SCIENTIFIC  THEISM 

The  vector  PCi,  therefore,  describes  equal  angles  in  equal 
times.  The  converse  may  readily  be  shown  to  be  true  ;  that 
is,  if  the  vector  describes  equal  angles  in  equal  times  the 
locus  is  a  conic. 

An  important  deduction  may  be  made  from  the  above 
conclusions.  Since  the  area  A  of  the  elliptic  sector  KDtP 
is  given  by 


r>A  PK.PA.GCi  , 

—  .PK.PA-     -2  --         -,  where 


/°Cl\ 

^J- 

*  T-  180°  =  radians  in  1°,  it  follows  that  in  circular  measure, 
with  oca  given  in  radians, 


and  since 


is  a  constant,  the  area  described  by  the  elliptic  vector  PD, 
depends  upon  and  varies  with  the  circular  vectorial  angle 
KPCi  =  oc  j.  Since  these  circular  vectorial  angles  are 
described  in  equal  times,  it  follows  that  the  elliptic  vector 
PDi  describes  equal  areas  in  equal  times.  This  is  Kepler's 
law  of  areal  velocities.  It  has  been  derived  without  the 
erroneous  Newtonian  central  mass  attraction  idea,  which 
hypothesis  is  incapable  of  showing  a  physical  reason  for  the 
modification  of  the  orbit  from  a  circular  into  one  of  variable 
radial  vectors.  A  single  central  force  cannot  produce  this 
modification.  In  assuming  the  two  unequal  force  factors 
Fv  and  Fx,  we  at  the  outset  provide  a  physical  basis  for  the 
mathematical  results  which  follow. 

We  shall  present  the  matter  from  still  another  stand- 
point. At  the  end  of  the  time  tt  we  shall  assume  the  vector 
PCt  to  be  in  the  location  shown  in  Fig.  21,  with  its  vectorial 
angle  =  cCj.  We  shall  further  suppose  that  the  moving  body 
is  actuated  by  the  outward  acting  forces  —  Fv  and  — '•  Fx. 
Opposed  to  these  forces  are  resistive  inward-acting  forces 
-f-  Fv  and  -|-  Fxt  parallel  respectively  to  the  Y  and  X  axes. 
These  forces  are  constant.  The  moving  body  actuated  by 
the  two  force  factors  is  subjected  to  a  simultaneous  two- 
directional  displacement  whose  limits  are  PK  and  PA,  re- 
spectively commensurate  with  the  forces  Fy  and  Fa.  Under 


SCIENTIFIC  THEISM  223 

the  action  of  these  constant  forces  the  body  will  be  subjected 
simultaneously  to  an  oscillatory  displacement  parallel  to  the 
Y  and  the  X  axes.  The  dynamic  relations  developed  for  the 
body  in  the  orbit  KHR  will  hold  simultaneously  for  both 
forces  because  they  are  constants  acting  against  resistive 
forces. 

Let  the  body  at  the  end  of  a  period  of  time  tt  be  found  at 
point  Dj.  Then,  in  respect  to  Fv,  point  Di  must  lie  in  a  line 
CiM  parallel  to  the  X  —  axis.  In  respect  to  the  force  Fxt 
point  Di  must  lie  in  a  line  DXJ  parallel  to  the  Y  —  axis. 
The  time  of  the  quarter  oscillation  (complete  period  -f-  4) 
PK  is  assumed  equal  to  the  time  of  the  quarter  oscilla- 
tion PA. 

Now,  since 


where  vv  and  vz  are  the  velocities  of  the  body  moving  in  the 
orbits  KCiB  and  RGiA  respectively. 

But    —  =  y  '  .,   where  s   and  sx  are  the 
vx    sx-J-t' 

respective  orbital  arc  distances.    Consequently, 


arc  RGi~~s,"~Fs' 

This  relation  is  true  only  when  Gt  lies  upon  the  vector 
CiP.  Therefore  the  line  DiJ  parallel  to  the  Y  axis  must  pass 
through  point  Gv  It  follows,  therefore,  in  light  of  the  pre- 
vious disclosures,  that  D,  is  a  general  point  in  the  conic 
which,  in  this  case,  is  an  ellipse.  Moreover,  the  law  of  areal 
velocities  is  a  direct  consequence  of  the  above  relations. 

We  have  referred  to  the  fact  that  a  complete  investiga- 
tion of  any  material  system  interacting  according  to  the 
Space-Time  Potential  necessitates  a  reference  to  a  three- 
directional  system  of  axes. 

The  inclination  of  the  earth's  axis  to  the  plane  of  its 
orbit  shows  conclusively  that  a  third  force  factor  influences 
the  system.  Since  the  obliquity  of  the  ecliptic  —  that  is,  the 
angle  between  the  plane  of  the  ecliptic  and  the  earth's  equa- 
torial plane  —  is  about  23°  27'  8",  the  angle  which  the  earth's 


224  SCIENTIFIC  THEISM 

axis  makes  with  the  ecliptic  is  about  66°  32'  52".  This  angle 
is  practically  constant  during  the  earth's  elliptical  motion  in 
the  plane  of  the  ecliptic.  Since  the  earth's  semi-diameter 
(according  to  Bessel)  is  20,923,597  feet,  the  distance  h  along 
a  normal  to  the  plane  of  the  ecliptic  from  the  most  remote 
point  of  the  earth's  equatorial  circumference  is  8,327,260 
feet.  During  one  complete  revolution  of  the  earth  about  its 
axis  this  point  traverses  through  a  total  normal  distance 
—  4h  in  the  time  23  hours,  56  minutes,  and  4  seconds 
=  86,164  seconds.  For  the  distance  h  the  time  is  21,541 
seconds.  This  corresponds  to  an  acceleration  a  =  0.035892-f- 
feet  per  second  squared,  along  the  normal  to  the  ecliptic, 

since    a  =  77.     It  is  therefore  clear  that  the  obliquity  of  the 

C 

ecliptic  cannot  be  maintained  without  the  continuous  activ- 
ity of  a  third  directional  force. 


SCIENTIFIC  THEISM 


225 


226 


SCIENTIFIC  THEISM 


SCIENTIFIC  THEISM 


227 


APPENDIX  B 

ELECTRICAL  RELATIONS  ACCORDING  TO  THE  DYNAMICS  OF 
THE  SPACE-TIME  POTENTIAL 

127.    The   Newtonian   Gravitational   Relation  According  to 

Dynamics. 

It  is  our  purpose  now  to  consider  the  Newtonian  expres- 
sion for  gravitational  attraction  in  connection  with  the  re- 
quirements of  dynamics. 

Consider,  then,  the  forces  f  and  F  acting  at  the  two 
points  A  and  C  shown  in  Fig.  22.  We  use  the  term  "force" 
here  in  its  ordinary  physical  sense,  without  entering  into  the 
consideration  of  the  implications  involved.  The  work  done 

in  a  system  when  a  force  f  is  transported  through  a  dis- 
tance r  is  given  by  the  expression 

W=/r 

Therefore  if  the  force  fia  transported  to  the  point  B 

through  a  distance  (s  —  a;),  the  work  Wv  —  f  (s  —  x). 
In  the  same  way  the  work  W2  performed  in  translating  the 
force  F  to  the  point  B  through  a  distance  x  is  given  by 
W2  =  F  (x).  Let  us  also  assume  that  the  point  B  is  so  re- 
lated to  the  entire  system  that  Wt  =  W»  =  f  (s  —  x)  = 
F  (x) .  We  can  regard  point  B,  then,  as  a  neutral  point  in 
the  system.  Moreover,  we  shall  suppose  that  the  time  t 

required  to  transport  /"to  the  point  B  is  equal  to  the  time  t 
necessary  to  translate  F  from  C  to  B.  We  can  write  the 
expression  F  (x)  =  f(s  —  x)  in  the  following  manner: 

/(s)  -  (F+/)x     (1). 

r                              2(s  — x) 
The   acceleration    a    of  J  is  therefore,  ft»-^a — - (2). 

2x 
and  the  acceleration  6  of  F  is,  b  =  —j (3). 

228 


SCIENTIFIC  THEISM  229 

It  is  evident  that  the  above  expressions  for  acceleration 
assume  that  /"and  F  start  simultaneously  from  rest.  If  the 
mass  concentration  at  A  is  m,  and  at  C,  M,  we  have 

f=  m  (a),  and  F  =  M  (b) (4) 

Considering  the  system  shown  in  Fig.  23,  we  there  assume 
*  mass  concentration  at  A  equal  to  the  expression  — — , 

and  similarly  at  C  we  locate  a  mass  concentration  of  the 
same  mathematical  magnitude.  The  significance  of  this 
procedure  will  be  apparent  in  the  succeeding  development. 
With  these  values  for  the  mass  concentration  we  obtain 

/Mm,  .          ,     „     Mm/, , 
=  -^-(a)     and     F  =  — ^-(b). 
S  S 

Introducing  the  values  for  a  and  6  given  in  Equations  2  and  3 

into  these  expressions, 

..M 

and    F 


See  Fig.  23. 

Substituting  these  values  of  f  and  F  in  Equation  1,  we  have 
As)=  [M™|2*1  ,  Mmf2(s-x)h  x 

Simplifying  and  solving  the  above  expression  for  f  we  find, 

2xrMm1 
^-—    = 


Consequently,  /  —  F  ;  a  =  6,  and  x  =  (s  —  x)  ,  and  point  B 
is  the  mid-point  of  the  span  AC. 

The  expression  bl  —  —\  is  of  the  Newtonian  type  for  two 

masses  M  and  m  at  a  distance  s  from  each  other. 

Let  us  concentrate  the  mass  m  at  A  and  M  at  C  in  the 
system  shown  in  Fig.  22.  Retaining  the  same  values  for 
accelerations  and  distances  and  proceeding  as  above,  we  now 

find  for  the  value  /"the  expression  : 

/•_b{M(x)+m(s-x)}  .^ 

J  s 

In  the  above  analysis  we  have  used  the  fundamental 
equations  of  motion,  force,  and  work,  which  can  be  shown 


230  SCIENTIFIC  THEISM 

to  be  true  by  experimental  evidence.  We  do  not  intend  to 
abandon  their  use  for  the  very  reason  that  they  can  be 
experimentally  verified.  Their  employment,  in  conjunction 
with  the  Newtonian  expression,  has  brought  us,  however, 
face  to  face  with  a  serious  dilemma.  We  have  derived  Equa- 
tion (5),  which  is  in  the  Newtonian  form,  by  employing 
these  very  fundamental  and  experimentally  demonstrable 
laws  of  motion,  force  and  work;  nevertheless,  the  derived 
expression  (Equation  5),  according  to  Newton,  should  have 
been  derived  from  the  system  shown  in  Fig.  22.  The  appli- 
cation of  these  same  fundamental  equations  to  the  system 
shown  in  Fig.  22  gives  us  a  radically  different  expression  for 

f  in  Equation  6,  involving  the  sum  of  the  masses  and  the 
distance  to  the  inverse  first  power.  It  is  seen  that  Equation 
5,  the  Newtonian  type,  can  be  correctly  developed  only 
under  the  assumption  that  the  mass  concentration  is  equal 
to  the  force  divided  by  the  acceleration,  which  is  as  it  should 
be  according  to  the  fundamental  laws  of  motion,  force,  and 
work.  When  we  apply  this  relation  between  mass,  accelera- 
tion, and  force  to  the  Newtonian  system  of  Fig.  22,  we 
derive  an  expression  entirely  foreign  to  the  Newtonian 
conception. 

128.     The    Fundamental    Function    of    Non-Newtonian    Dy- 
namics. 

Our  interest,  therefore,  must  be  centered  upon  the  more 
primitive  function,  the  anti-differential  of  the  Newtonian 

-.  variation,  that  is,  the  expression  given  by, 

8 


If  we  desire  mechanically  to  reconstruct  the  universe,  I 
feel  certain  that  this  can  be  most  truthfully  accomplished 
by  thinking  of  interdependent  activity  centers  as  space- 
time  projections  of  dynamic  mass.  To  this  space-time  pro- 
jection of  interacting  mass-acceleration  kerns  I  have  given 
the  name  of  "space-time  potential."  This  conception  in- 
volves the  postulate  that  every  position  in  the  universe  has 
a  definite  potential  coefficient  and  that  displacement  in  the 
Space-Time  Projection  is  commensurate  with  the  magnitude 


SCIENTIFIC  THEISM  231 

of  the  equilibrating  readjustment  involved  in  this  activity. 
This  view  eliminates  the  ether  as  a  necessary  medium  of 
propagation  and  communication  of  physical  activities. 
For  reasons  already  stated,  we  abandon  the  Newtonian 

-    function  and  proceed  to  the  investigation  of  its  integral, 

D 

the  function  which  we  maintain  is  the  true  function  of 
activity  variations  in  our  interacting  system  made  mani- 
fest in  the  Space-Time  Potential. 

Let  A  and  B,  Fig.  24,  be  two  activity  factors  in  an  inter- 
acting system.  Let  the  known  distance  between  them  be  d. 
Let  the  intensity  7d  of  this  specific  interaction  for  the  known 
distance  d  be  dependent  upon  the  distance  between  the  two 
activity  factors  in  such  a  manner  that  the  intensity  of  inter- 
action If  for  any  variable  distance  s  between  the  activity 
factors  A  and  B  varies  inversely  with  the  distance  s  be- 
tween them. 

Then  7  will  vary  as  —  if  there  be  no  other  change  in  the 

*  s 

other  factors  of  the  system.  Consequently,  for  a  known  dis- 
tance d, 

"d-=kA 


where  k  is  a  constant  which  can  be  experimeri tally  determined 

Furthermore,  since  k  =  Id(d),  it  follows  that  if  the  constant 

k  can  be  determined  for  unit  factors,  we  can  determine  the 

intensity  7.  by  investigating  the  expression  -.     It  is  evident, 

S 

therefore,  that 


If  we,  for  purposes  of  analysis,  make  fc-=l  in  the  above 
expression,  we  obtain 


This  equation  may  be  written  y  =  -  if  we  regard  the  in- 

X 

tensities  as  ordinates  parallel  to  the  Y  axis  and  the  distances  8 
as  abscissas  parallel  to  the  X  axis  in  Fig.  25.  It  is  evident  that 
this  is  the  expression  for  an  hyperbola.  The  area  between  the 

vertical  ordinates  x  =  o  and  x  =  l   and  the  hyperbola  j/*»-   is 

x 


232  SCIENTIFIC  THEISM 

given  by 


1"' 


-dx  =  logex    =  loge(l)  — loge(a)  =  0.0  -  logea. 

./.-.  Jx-a 

As  a  approaches  o,  the  limit  of  loge  (a)  approaches 
infinity.  In  other  words,  a  definite  finite  value  for  the  re- 
quired area  does  not  exist ;  that  is, 


L 


x-l 

-dx  =*  —  oo 

X 


Consequently  the  area  between  x  =  1  and  x  =  a,  where  a 
is  not  =  0,  is  given  by  the  expression  : 

—log,  A 

(the  constant  of  integration  has  been  omitted  throughout 
the  above)  .  Similarly,  the  area  between  x  =  1  and  x  =  b 
is  given  by  : 

-b 

dx-0+loge(b) 

1.0 

The  work  W  done  in  the  displacement  of  B  in  the  inter- 
acting system  of  Fig.  24  is  given  by 


A 

/*-: 


1  1 


1.  da.     Substituting  in  this  expression  the  value  for 
I.  =  K(  -  J  and  integrating,  we  obtain 

W=  IkAYb-k.fefe*  ..............................  (8). 

Therefore  the  work  done  in  the  displacement  of  the  activity 
factor  B  from  a  position  s  =  1  to  a  position  s  =  2  is 


that  is, 


W  Uk|loge2-logeU  =k.logJji  =  a   constant (9). 

In  general,  wT^k.logJ-i (10). 

_la=m  (mj 

It  follows  that  every  system  existing  in  dynamic  equilib- 
rium involves  a  constant  work  factor.     Consequently,  for 


SCIENTIFIC  THEISM  233 

any  given  system,  W  =  F  (s)  =  (Ma)  s  =  a  constant. .  (11) 
In  Equation  11,  F,  is  the  force  exhibited ;  M  is  the  mass ;  a 
is  the  acceleration,  and  s  is  the  distance.  Every  activity 
system  strives  continuously  for  a  realization  of  this 
condition. 


129.  The  Change  Point. 

If  we  plot  these  constants  from  some  suitable  point  as  a 
center,  preferably  the  point  which  causes  loges  to  equal 
zero,  we  obtain  a  series  of  concentric  semi-circular  lines 
each  of  which  pertains  to  a  particular  constant.  The  point 
1,  for  which  loge  st  =  o,  divides  the  system  into  positive 
and  negative  work  zones  within  which  dynamic  and  static 
equilibrium  is  established.  To  this  particular  point  (point 
1)  we  have  given  the  name  change  point.  The  circular  lines, 
each  defined  by  a  specific  constant,  may  be  termed  loci  of 
equal  potentials.  In  Fig.  26  we  show  the  logarithmic  curve 
plotted  with  values  of  loge  s  as  ordinates  for  corresponding 
values  of  s  as  abscissas.  Fig.  27  also  shows  a  typical  Space- 
Time  Potential  zone  system.  The  data  for  Figures  26  and  27 
are  found  in  Table  1. 

The  element  of  time  has  not,  up  to  this  point,  entered  into 
our  consideration.  If  the  motor  activity  factors  in  the  sys- 
tem remain  unchanged,  we  must  assume  that  the  magnitude 
of  the  work  effect  for  one  unit  of  time  must  be  the  same 
as  for  every  succeeding  unit  of  time. 

If  a  system  is  to  continue  to  exist  in  the  state  of  dynamic 
equilibrium,  the  sum  of  the  positive  and  negative  work  done 
must  be  equal  to  zero.  A  system  rotating  about  the  change 
point  1  would,  moreover,  continue  to  rotate  unless  dis- 
turbed by  new  influence  factors.  Furthermore,  the  path  of 
motion  would  be  along  loci  of  equal  potential.  The  positive 
work  done  about  the  center  of  rotation  (the  change  point 
1)  would  for  every  interval  of  time  be  equal  to  the  negative 
work  done.  Each  succeeding  unit  of  time  must  develop 
equal  amounts  of  work, 

130.  Rotary  Systems. 

In  a  simple  rotary  system,  Fig.  28,  consisting  of  the  two 
bodies  M  and  m  rotating  in  dynamic  equilibrium  about  the 


234  SCIENTIFIC  THEISM 

change  point  1,  the  positive  work  done  in  a  unit  of  time  by  m 
in  passing  from  the  position  ra0  to  mx  must  be  equal  to  the 
negative  work  done  in  a  unit  of  time  by  M  in  passing  from 
M0  to  Mt.  Furthermore,  the  positive  work  done  from 
m0  to  rax  must  be  equal  to  the  positive  work  in  a  unit  of 
time  from  rax  to  w2.  Similarly,  work  M0  to  M ^  =  work 
M i  to  M 2,  if  the  time  element  is  the  same. 

If  the  bodies  M  and  m  are  assumed  as  constants  in  the 
system,  then  their  orbits  will  continue  to  be  concentric 
circles  unless  a  third  activity  factor  be  introduced  into  the 
system.  If  M  and  m  remain  constant  and  a  change  from  the 
circular  orbits  is  observed,  then  the  cause  for  this  change 
cannot  be  found  within  the  simple  system  M  —  m.  More- 
over, a  central  force  does  not  exist  in  the  universe.  Condi- 
tions of  dynamic  equilibrium  exist,  but  no  single  factor  in 
the  system  can  be  regarded  as  a  central  force.  The  time- 
honored  notion  that  the  sun,  a  central  force,  is  located  at 
one  focus  of  an  ellipse  with  the  earth  in  the  elliptic  locus 
is  nothing  but  a  convenient  mathematical  myth.  The  point 
1  may  be  found  within  the  limits  of  the  volume  M,  but  it  is 
not  coincident  with  the  center  of  mass  of  M .  If  the  two 
points  are  practically  coincident  the  continuous  neutraliza- 
tion of  the  distance  involved  between  them  must  be  ascribed 
to  other  activity  factors  not  depicted  in  the  simple  system 
shown  in  Fig.  28.  If  we  grant  that  the  sun's  center  of  mass 
is  located  at  point  1,  that  fact  alone  would  not  account  for 
the  deflection  of  the  earth's  path  from  a  circular  to  an  ellip- 
tic orbit.  A  cyclical  change  in  the  mass  of  either  M  or  m  (or 
both)  would  constitute  a  sufficient  cause  for  a  change  in 
the  orbits  from  the  circular  to  the  elliptical.  However,  we 
are  not  assuming  that  such  a  rhythmical  mass  change 
occurs,  consequently  the  elliptical  orbit  must  be  due  to  influ- 
ences not  contained  in  the  arbitrary  and  simple  system 
M  —  m. 

The  sum  total  S  of  all  the  activity  factors  in  the  inter- 
acting system  known  as  the  universe  may  be  represented  by 
the  expression,  S  =  R  -\-T,  where  r  is  the  system  M  —  m, 
and  R  is  all  the  remaining  factors.  It  is  not  necessary  to 
assume  that  all  of  R  is  directly  involved  in  interaction  with 
the  system  r;  but  in  order  to  simplify  the  problem  we  may 
think  of  the  unequilibrated  portion  U  of  R  which  requires 


SCIENTIFIC  THEISM  235 

the  system  r  for  its  equilibrant.  It  is  to  the  system  U,  then, 
that  we  must  ascribe  any  actual  modifications  from  the  cir- 
cular orbits  which  may  be  observed  in  the  system  r.  We 
shall  assume  that  the  system  r  will  endeavor  to  maintain  its 
own  fundamental  nature  while  under  the  interacting  influ- 
ence of  U.  We  believe  that  such  an  assumption  is  more 
rational  than  the  converse,  and  has  the  advantage  of  being  in 
line  with  the  reasonable  ideas  of  conservation.  In  dynamics 
the  path  of  a  particle  is  of  secondary  importance  since  an 
infinite  number  of  component  paths  may  produce  the  same 
resultant.  Consequently  we  feel  that  we  are  justified  in 
supposing  that  the  basic  element  of  the  system  is  the  ele- 
ment of  work  done,  which  we  have  shown  is  a  constant  for  a 
unit  of  time.  If  the  converse  of  this  is  assumed,  it  would 
follow  that  in  the  equilibrated  system  r  work  is  created  in 
time  without  a  change  in  U  or  R.  The  latter  position  would 
be  difficult,  indeed,  to  substantiate. 

For  these  reasons  we  look  for  deflections  and  velocity 
changes  in  the  orbit,  but  we  maintain  that  the  system  r 
will  continue  to  exhibit  its  basic  characteristic,  which  is 
the  development  of  equal  work  areas  in  equal  times.  If  the 
previously  developed  equation  of  an  ellipse  is  considered, 
it  will  be  seen  that  this  conic  section  satisfies  the  condition 
that  the  developed  work  areas  shall  be  equal  for  equal  inter- 
vals of  time.  This  condition  is  shown  in  Fig.  29,  where  the 
path  of  m  is  deflected  from  the  circular  path  by  the  influence 
U  on  the  orbit  m^m^m^  consistent  with  the  condition  that 
the  area  described  by  the  radius  vector  shall  be  constant 
for  a  unit  of  time.  Thus  area  (Im0m/)  =  (area  lm/w«), 
etc. 

The  Newtonian  justification  of  Kepler's  equal  time-area 
law  was  based  upon  the  assumption  of  a  central  force  acting 
from  the  focus  of  the  conic  section  with  an  intensity  which 
depended  upon  the  product  of  the  masses  and  inversely 
upon  the  square  of  the  distance  between  them.  Finding 
no  rational  or  empirical  justification  for  the  Newtonian 
formula  and  failing  to  agree  with  him  in  regard  to  the 
efficacy  of  a  single  unchanging  central  force  to  deflect  a 
body  into  an  elliptic  orbit,  we  have  made  radically  different 
assumptions  which  lead  to  the  same  final  results  as  far  as 
observed  phenomena  are  concerned. 


236  SCIENTIFIC  THEISM 

131.  Electron  Theory  According  to  the  Space-Time  Potential. 
We  shall  now  show  that  the  Space-Time  Potential  is 

applicable  to  atomic  and  electronic  conditions.  In  order  to 
test  the  applicability  of  the  system  outlined  above,  let  us 
attempt  the  calculation  of  the  so-called  electrical  charge  on 
the  electron. 

We  have  already  seen  that,  in  our  system  of  Space- 
Time  Potential,  every  case  of  interaction  involves  a  work 
constant.  We  have  expressed  this  fact  mathematically  by 

the  relation         „,.      ,,,  x 

W  =  (Ma)  s  =  a  constant. 

Moreover,  every  activity  system  will  so  conduct  itself  in  its 
various  factor  activities  that  the  realization  of  this  work 
constant  becomes  an  accomplished  fact  unless  extraneous 
factors  intervene,  in  which  event  the  law  still  holds,  pro- 
vided that  the  additional  factor  be  included  in  the  system. 
Gas  expansion  relations  come  under  the  Space-Time 
Potential.  If  the  temperature  remains  constant  during  ex- 
pansion we  know  that  p  v.  =  a  constant,  where  p  is  the  pres- 
sure exerted  and  v  is  the  volume  of  the  gas.  The  phe- 
momena  of  thermodynamics  are  explainable  according  to 
the  Space-Time  Potential.  The  increase  in  internal  energy 
developed  when  a  system  passes  from  the  state  1  to  the 
state  2  can  be  calculated  from  the  Space-Time  Potential. 
The  work  done  in  compression  is  merely  the  reverse  prob- 
lem of  the  case  of  expansion.  In  this  respect,  also,  our 
Space-Time  Potential  is  more  far-reaching  than  Newton's 
formula. 

132.  Calculation  of  the   Charge  Exhibited  by  an  Electron, 
Using   the   Primary   or   Hyperbolic   Relations   of   the 
Space-Time  Potential. 

If  our  Space-Time  Potential  is  to  pass  still  further  be- 
yond the  Newtonian  limitations,  we  must  show  its  applica- 
bility to  electrical  phenomena.  Let  us  attempt  the  calcula- 
tion of  the  electrical  charge  on  an  electron  by  using  our 
fundamental  relation 

W  =  (Ma)s  =  C,  a  constant 

In  order  to  simplify  the  analysis,  we  shall  write  the  ex- 
pression in  the  form 

MR  =  C,  where  R  =  a.s 


SCIENTIFIC  THEISM  237 

An  operative  electrical  work  system  involves  a  pressure 
constant.  The  liberation  constant  of  an  electron  must  con- 
sequently involve  a  decomposition  constant  D,  consequently, 
R  =  Dr,  where  D  is  the  decomposition  voltage  and  r  is 
the  intensity  of  the  current  during  the  time  t.  Substituting 
this  value  for  R  in  the  expression  MR  =  C,  we  obtain, 

M(Dr)  =  C  or  Mr  =  -^  =  h, (12) 

since  D  is  a  constant  for  any  given  system.  If  the  intensity 
of  the  current  r  is  given  in  amperes  and  the  time  t  is  ex- 
pressed in  hours,  then  our  compound  unit  is  the  ampere- 
hour.  We  must  also  relate  the  intensity  of  fhe  current  to 
its  dissociative  effect  in  the  electrolytic  cell,  since  this  is  the 
very  means  employed  in  measuring  current  intensities.  The 
value  r,  then,  for  any  particular  chemical  element,  becomes 
the  number  of  ampere  hours  necessary  to  liberate  a  unit 
mass,  the  gram,  per  unit  of  chemical  valence.  Moreover, 
since  the  liberated  masses  must  be  in  the  same  ratio  as  the 
atomic  masses  of  the  chemical  elements  considered,  it  fol- 
lows that  M  may  be  expressed  in  terms  of  the  atomic  masses. 

The  expression  Mr  =  h  may  be  written 

M  =  h    (1)    (13) 

In  Table  II  we  give  the  values  of  M  and  r  for  a  sufficient 
number  of  chemical  elements  to  plot  the  curve  shown  in 
Fig.  30,  where  M  is  plotted  as  ordinates  for  the  correspond- 
ing values  of  r  as  abscissas.  The  curve  in  Fig.  30,  is  an 
hyperbola  of  identically  the  same  order  as  the  one  shown 
in  Fig.  25,  derived  for  the  Space-Time  Potential.  Here  we 
have  arrived  at  magnitudes  of  atomic  and  electronic  pro- 
portions, and  we  still  find  the  function  /=k  f  — )  opera- 
tive, while  the  Newtonian  function  /==k  (— )  fails  us 

completely. 

By  the  use  of  our  own  function  we  can  derive  the  value 
of  the  charge  shown  by  an  electron.  In  order  to  accom- 
plish this  we  shall  adopt  the  well-established  value  of 
1.662xlO~24  gram  as  the  mass  H  of  the  hydrogen  atom.1 
The  remarkable  researches  of  Kaufmann  have  shown  that 

'Robert  A.  Millikan,  The  Electron  (1917),  p.  238. 


238  SCIENTIFIC  THEISM 

the  mass  of  the  electron  is  not  a  fixed  quantity,  but  that  it 
varies  with  the  velocity,  increasing  as  the  velocity  increases. 
This  is  in  complete  accord  with  the  laws  of  the  Space-Time 
Potential,  as  will  be  seen  by  inspecting  Table  I  and  Fig. 
27.  Moreover,  the  Space-Time  Potential  offers,  for  the  first 
time,  an  explanation  of  the  very  phenomenon  brought  to 
light  by  the  researches  of  Kaufmann.  Since  this  variation 
of  mass  with  velocity  is  known  to  be  a  fact,  and  since  the 
values  for  the  mass  are  practically  constant  up  to  a  velocity 

of  r«that  of  light  (3.0  X  1010  centimeters  per  second  in 

air),  we  shall  use  in  our  analysis  that  value  of  ra  for  the 
electron  which  corresponds  to  a  velocity  v  =  3.0  x  10 9 
=  0.1  (3.0  X  1010) ,  the  velocity  of  light  in  air. 

For  this  velocity  the  mass  ra  of  the  electron  is  about 

of  the  mass  of  the  hydrogen  atom,1  hence 

4 
=9.0081X10~28  gram (14). 

If  D,  the  liberation  potential  difference  for  the  electron, 
and  e,  the  charge,  are  known,  then  ra  may  also  be  calculated 
from  the  expression 

2eD 
m  =  -^r (15). 

By  using  the  well-known  relations  pertaining  to  electro- 
chemical equivalence  we  have  calculated  the  quantities  set 
forth  in  Tables  II,  III,  and  IV.  The  relation  of  these  values 
to  the  curve  of  constant  areas,  which  is  of  the  utmost  signif- 
icance to  the  development  of  the  Space-Time  Potential,  is 
evident  from  an  inspection  of  Fig.  30.  We  shall  now  de- 
velop the  value  of  the  charge  e  carried  by  an  electron  from 
the  Faraday  relations  and  by  the  use  of  the  data  contained 
in  the  tables  referred  to  above. 

Faraday's  first  law  states  that 

uC  =  j (16). 

where    u  =  a  constant  depending  only  upon  the  kind 

of  the  substance, 

C  =  the  current  passing  through  the  electrolyte, 
ra  =  the  amount  of  the  liberated  mass,  and 
t  =  the  time  of  duration  of  the  current  C. 
•Robert  A.  Millikan,  The  Electron  (191?),  P-  184. 


SCIENTIFIC  THEISM  239 

The  value  u  is  called  the  electrochemical  equivalent,  and 
in  Table  II  the  values  of  u  are  given  for  the  different  ele- 
ments, with  m  in  grams,  t  in  seconds,  and  C  in  amperes. 

Since  1  ampere-hour  =  3600  coulombs,  where  1  coulomb 

=  1  ampere  in  1  second,  it  follows  that  u  =   og-/xTt   gram, 


where  R  is  in  ampere-hours  per  gram  per  unit  valence. 
This  is  evident  because  3600R  coulombs  are  required  to  lib- 

erate 1  gram  of  the  given  substance.    The  function  ~  there- 

Jtv 

fore  becomes  the  fundamental  relation  from  which  our 
analysis  begins.  That  this  function  is  our  original  Space- 
Time  Potential  function  associated  with  proper  constants 
is  evident  when  we  consider  the  motion  of  the  liberated  ion 
in  the  electrolyte  as  being  a  case  of  genuine  motion  in  a 
work  system  which  must  operate  in  accordance  with  the 
fundamental  laws  of  the  Space-Time  Potential. 
The  values  u  and  M  are  related  by  the  expression 

-£=k,  a  constant=0.  00001044  ...............  (17) 

that  is,  «  =  kM  =  grams  per  coulomb  ;  hence,  if  we  use  as  the 

IcriO 

atomic  mass  of  the  electron,  we  have 

u  =  0.00001  044  X-r£-rv-8rams  Per  coul°mD  for  the  electron. 


If  u'  is  the  grams  liberated  by  1  electrostatic  unit  (C.G.S.)i 
u'=      u      because  1  coulomb  =3xl09  C.G.S. 

O  XN  HJ 

electrostatic  units,  and  the  valence  v  =  1  ................  (18). 

Therefore, 

u          0.00001044 


If  N  =  number  of  electrons  liberated  by  1  C.G.S.  electrostatic  unit, 
m  =  the  actual  mass  of  the  electron  in  grams  =  9.0081  X 
10" 28  gram,  we  have 

u' 

N  =—= number  of  electrons  liberated  by  1  C.G.S. 
m 

electrostatic  unit (19). 

N     1.8861X10-" 
9.0081XlO~M 
=  2,093,800,000  =  2 . 0938  X 10+9  electrons. 


240  SCIENTIFIC  THEISM 

If  e  is  the  electric  charge  on  each  of  the  N  electrons,  it  follows  that 
Ne  =  1  C.G.S.  electrostatic  unit  ....................  (20), 

because  one  such  unit  of  electricity  is  required  to  liberate  the  N 

electrons. 

Therefore, 

~=  _£  --  ±  _  —A  77fiy  m-10  ens 
N~2.  0938X10+' 

electrostatic  unit  .................................  (21). 

Let  us  attack  the  problem  from  another  viewpoint,  which  will 
introduce  new  and  interesting  constants. 

By  referring  to  Table  III,  we  see  that  u'  =  k'M  and  therefore 


(22). 


1845 

The  value  k'  is  a  constant  and  could  have  been  derived  from  any 
of  the  given  elements  by  taking  the  corresponding  values  of  u' 
and  Af. 

If  M  is  the  atomic  mass  and  m  is  the  actual  value  in  grams  of 
a  given  element,  then  the  constant  ratio  is  given  by 
1 

^i-gWffio-"-6-01^*10*"  Av°gardro'8 

Constant  (H  =  1 . 0) (23). 

u' 
Now,  since  N  =  —  and  u'  =  k'M (24) 

by  substitution  we  obtain 

k'M  M 

N  =  ^^    but  — =1;  therefore (25). 

m  m 

N  =  k'l  =  3.480XlO-15x6.0168XlO  +  23=2. 0938x10+'...  (26). 
per  each  C.G.S  electrostatic  unit.  Since  k'  and  I'  are  both 
constants,  it  follows  that  N  is  a  constant. 

Since  Ne  =  1     and  N  =  k'l,  it  follows  that 

e=  jpj  =4. 775X10- 10  C.G.S.  electrostatic  units (27). 

As  before,  we  reason  that  e  must  be  a  constant  since  both  k' 
and  I  are  constants. 

These  facts  can  therefore  be  expressed  as  general  laws : 

1.  The  number  of  ions,  whether  gaseous  or  liquid,  lib- 
erated by  a  given  quantity  of  electricity  is  a  constant  in- 
dependent of  the  kind  and  mass  of  the  ion. 

2.  The  charge  carried  by  a  free  ion,  whether  gaseous 


SCIENTIFIC  THEISM  241 

or  liquid,  is  a  constant  quantity  independent  of  the  kind  and 
mass  of  the  ion. 

The  following  values  of  e,  derived  experimentally,  show 
that  our  own  value  derived  from  the  application  of  our 
Space-Time  Potential  is  concordant  with  experimental 
facts  : 

H.  A.  Wilson  .....  e  =  3.1  xlO-10  C.G.S.  electrostatic  unit 
J.  J.  Thomson  ----  e  =  3.4xlO-10  C.G.S.  electrostatic  unit 
E.  Rutherford  ----  e  =  4.65  xlO-10  C.G.S.  electrostatic  unit 
R.  A.  Millikan.  .  .  .  e  =   4.774  ±   O.OOSxlQ-10  C.  G.  S.  elec- 

trostatic unit 

The  discrepancies  in  the  above  experimental  value  of  e 
are  due  to  the  differences  in  the  experimental  methods  em- 
ployed, and  also  to  the  variations  in  the  analytical  assump- 
tions. The  Millikan  value  of  e  is  probably  correct  within  the 
limits  given.1 

The  data  given  in  Table  III  can  be  used  to  calculate  the 
masses  of  the  various  ions.  Knowing  R,  the  C.G.S.  elec- 
trostatic units  per  unit  of  valence  necessary  to  liberate  one 
gram  of  an  ion,  the  mass  m  of  an  ion  may  be  found  from  the 
relations  given  in  Tables  III  and  IV  : 


r,  ^ 


In  the  above  relation  it  is  assumed  that  e  is  &  constant 
representing  the  charge  associated  with  the  mass  m  of  a 
given  ion  at  the  moment  of  liberation. 

The  fundamental  electrical  relations  involved  in  Tables 
II,  III,  and  IV  are  shown  as  a  hyperbolic  curve  in  Fig.  30. 
This  curve  is  of  the  same  order  as  the  curve  depicted  in  Fig. 
25,  which  constitutes  the  primary  or  fundamental  curve  of 
the  Space-Time  Potential.  The  secondary  work  curves,  simi- 
lar to  Fig.  26,  may  readily  be  derived  from  the  correspond- 
ing primary  hyperbolas.  It  is  therefore  evident  that  we 
have  dealt,  in  the  above  analysis,  with  relations  which  in- 
here in  the  fundamental  function  of  the  Space-Time  Poten- 
tial. Since  mr  =  e,  a  constant,  it  follows  that  the  electrical 
relations  are  of  the  same  order  as  the  volume-pressure  rela- 
tion which  pertains  to  gases.  In  other  words,  the  masses  of 


'Robert  A.  Millikan,  The  Electron  (1917),  p.  119. 


242  SCIENTIFIC  THEISM 

the  ions  are  related  to  the  electrical  charges  in  the  same 
manner  as  the  volume  of  a  gas  is  related  to  the  applied 
pressures. 

We  shall  now  calculate  the  charge  carried  by  an  electron 
from  the  secondary  relations  which  inhere  in  the  Space- 
Time  Potential.  By  secondary  relations  we  mean  those  re- 
lations which  may  be  evolved  from  the  analysis  of  the  work 
curve. 


SCIENTIFIC  THEISM 


243 


(J5-X) 


/sl 


Force 


rce  j  ex 
ntftu,  Ioni 


an  form. 


(S-X) 


-»J 


oo 


244 


SCIENTIFIC  THEISM 


SCIENTIFIC  THEISM 


245 


K. 


s 


ezr 

*•      //S-O-= 


9/C'O-*/* 


M  >. 

K]      <3 

c«  "^ 

11 

M 


*a 

^ 


=5%> 

COC'2- 


246 


SCIENTIFIC  THEISM 


SCIENTIFIC  THEISM 


247 


Fig.  30. 
Curve  of  Constant  Areas. 


248 


SCIENTIFIC  THEISM 


TABLC-I. 

Cot.   1. 

Col.  Z. 

Cot.  3. 

Co  6.  4. 

Co6.S~. 

Cot,.  6. 

Co6.7. 

Location 
Point. 

n 

Distance 
fe  C/lanfe 

Feint. 
«S 

MrtDcnc. 

"ISffl- 

"Wfl 

WodDoac. 

fyft 

ajrQiz 

Force 
^ 

Kli 

5 

n 

Katie. 
Distance. 
Velocity, 
tfcce/tratifi 
force. 

Mn> 
**> 

Hfrf(mJ 

p 

1 
n 

a 

0.00 

<0 

II 

/.oo 

-OO 

CO 

*  0.0000561492 

omxstft 

-9-7675 

9.  78005 

•+&  - 

5(7,185,  ooai^ 

f  O.OOOZ0596 

0.9957MM 

-8.  4878 

6A&955 

I3w 

ZJ,57^t9.H 

0.01 

O.S9 

-4.  60S 

4.65 

4. 

/Oj(W>mxg 

O.05 

0.95 

-Z.996 

3./S 

^^ 

4&0mto 

0.10 

1 

II 

* 
1 

^«. 

0.90 

-2.303 

>  0.694 
>  0.405 
>  0.288 
>O.ZZ3 
>0./8Z 
>0./54 
>0.&4 
>  O.I  76 
^0.105 

~VfO.IOS 
±0.693 

\0.40(> 
}-0.&7 

>  O.Z2* 
>0./83 
>0./5f 
>  0./35 
>  0.//8 
>O.IOb 

>  0.693 

>  0.405 
->0.Z88 

2.56 

T^*V 

/00m  ,o 

0.20 

0.80 

-/.  603 

Z.OI 

1—  JK?|  v_ 

SSms 

O.30 

0.70 

-/'JS04 

1.72 

^l<^ 

//.09ff!m 

0.40 

0.60 

-O.9/6 

1.53 

II 

6.25m*.5 

0.50 

O.50 

-0.693 

1.386 

^l^c 

4.oom  1.0 

0.60 

O.40 

-o.s// 

1.277 

^l^ 

2.789ffl/.u 

O-  70 

0.30 

-0.3J7 

/./9 

z.wsm/.n 

0.80 

o.zo 

-0.223 

/.// 

Olt^ 

/.S63M/2S 

0.9O 

o./o 

-0./OS 

/.OS" 

n 

f.ZSZmi.ii 

'    K 

ysf  QBE 

1.00 

mi.H 

J.//f 

0.11 

•f-  0.10  5 

0.9*5 

/.// 

m/.n 

1.25 

0.25 

-t-o.ezs 

0.89Z 

1.25 

mi  ts 

1.43 

0.43 

•f-0.357 

O.8ZO 

7.43 

m  1.13 

/.67 

0.67 

+0.  S// 

0.762 

/•67 

rn/.ti 

2.00 

/.oo 

+0.693 

0.633 

2.00 

m  z.ea 

£.50 

/.so 

+0.  9/6 

0.6/0 

2.50 

ffll.io 

3.00 

2.00 

+1.  099 

0.549 

3.00 

m  3.00 

3.33 

2.33 

+  1.204 

O.5/6 

3.33 

/77jM 

4.00 

3.00 

-f-/.366 

0.462 

4-OO 

7Jlf.cc 

ff.OO 

4.00 

•f-/.  609 

0.402 

S.OO 

m  s.oe 

6.00 

&.06 

+  /.79Z 

0.3584 

6-oc 

/n  t.oe 

7.00 

->. 

•jl 

(5! 

C 

II 
<0 

6.00 

+/.916 

0.324 

7-00 

m  7-et 

e.oo 

7.00 

+3.079 

0.297 

e.oo 

fll  f.eo 

3.00 

e.oo 

+£.  197 

0.274 

3.00 

ffl  3.00 

/o.oo 

3.OO 

+2.303 

0.256 

/o.oo 

ffl  10JX> 

20.00 

/9.06 

+2.996 

0./57S 

20.00 

m  3.0.™ 

.  zs.oo 

Z4.00 

+3.2/9 

0./34/ 

2S.OO 

/n  gf.to 

SO.  GO 

49.00 

+3.9/2. 

0.0798 

50.00 

7ft  Se.e 

75.OO 

74.00 

+  4.3/7 

0.0583 

75.00 

m  ?5.» 

/oo.oo 

99.00 

+4.  60  F 

0.0465 

/OO-  00 

7?1  /tt.o 

f      +855.20 

4854.V) 

+8.4-6  78 

9.00I74654 

4835.20 

m  t 

*•  /76  03-  70 

17808.70' 

-t-9.787S 

^MH 

/7809.  70 

m* 

n 

n-i. 

IS 

h^r(a-i). 

n 

7T?n- 

• 

8 

-f-oo 

+  <*> 

+  00 

o 

SCIENTIFIC  THEISM 


249 


TABLE-I.  CONTINUED. 

< 

I' 

f 

/ 
n 
0.  ooooo 

—  co 

0.90 

T/ie/ftfroctsm.  Titfion 

.,/     /   Uneout 
V                5S 

<%*'' 

-0./05 

J. 

0.999J80/ 

-«- 

^--" 

;^~ 

'^ 

*** 

1 

~/.9dx/0~f 

-<  —  —  limit  t/ffuaJRmtii  Or6its.  —  *\ 

S?      J-fl                 " 

X 

n 

r/fit 

rows- 

d 

0.99999567 

I'l'"^* 

-4.95x0"'  ' 

L 
c 

0.9999999907/3 

fr  f 

:.:r..i. 

i 

s, 

1 

CoL 

r" 
\ 

\ 
T~ 

^ 

^ 

i 
b 

0,999999993809 

^,'<* 

^^'  /                  X  ** 

_,[  _/.  .  . 

-6.I875X/0-* 

a 

0.999999996839 

\i 

-3.09375X/0'9 

l-fl 
a 

Change  Point. 

L   'r    "'    !'  '   <r 

0.0000 

i.mowMoi 

'         »        \ 
,\  \       JS.. 

'i    / 

,' 

/ 

> 

'S 

II 

s 

\ 

&1 
n 

+3.0937&/0'9 

<—  +  Limit  efEfuat  T=todii  Orbits.  —  >- 

I 

I.MMMMM9/ 

&  ^       K 

\        0^ 

f"^>|f 

+6.I875X/0-9 

c 

l.oooomomi 

II 

•£3.Z8/25x/0'9  < 

d 

1.00000193 

^    ^S. 

! 

+$95x/0~* 

e 

/.  0000/98 

X 

| 

+/.98X/0-* 

1  1 

s. 

^ 

§ 

/ 

/./// 

— 

•" 

+0./05 

n. 

Tnff 
7?e0t  0>t   6f 

Macrocosm. 

§> 

l//tefu&S  Ttaett't 

Or&its. 
T/ie  Microcosm  . 

» 

( 

250 


SCIENTIFIC  THEISM 
TABLE  II 


Elements. 

JS 

i 

OQ 

V. 

1 

03 
> 

M. 

O   to 

•"*     Q} 

O     ffi 

Is 

U. 

TT  _  ,              ,  _  rrvj 

R. 

Ampere 
—  Hours 
per  Gram 
per  Unit 
Valence. 

M, 
M    -M 

h. 
h-M,R. 

Hydrogen 
Constant. 

3600  R     KMl 
Electrochemical 

Equivalents 
per  Unit  Valence 
Grams   per 
Coulomb. 

V 

Chemi- 
cally 

Equiv- 
alent 
Atomic 
Masses. 

Electron 

E 

1 

1 

1845 

0.00000000566095 

49069.06 

1 
1845 

26.5957 

Hydrogen 

H 

1 

1.000 

0.00001044 

26.5957 

1.000 

26.5957 

Carbon 

C 

4 

11.91 

0.0000310 

8.9606 

2.977 

26.5957 

Nitrogen 

N 

3 

13.93 

0.0000484 

5.7405 

4.643 

26.5957 

Oxygen 

0 

2 

15.88 

0.0000829 

3.3512 

7.940 

26.5957 

Sodium 

Na 

1 
1 

22.88 

0.0002388 

1.1632 

22.88 

26.5957 

Potassium 

K 

38.86 

0.0004052 

0.6855 

38.86 

26.5957 

Iron 

Fe 

2 

55.5 

0.0002902 

0.9576 

27.75 

26.5957 

Copper 

Cu 

1 

63.1 

0.0006586 

0.4218 

63.10 

29.5957 

Silver 

Ag 

1 

107.12 

0.0011180 

0.2485 

107.12 

26.5957 

Platinum 

Pt 

2 

193.3 

0.0010094 

0.2752 

96.65 

26.5957 

Lead 

Pb 

2 

205.35 

0.0010718 

0.2592 

102.675 

26.5957 

Important  Relations 
U  =      *  '       gram.    K  =«-=  0  •  0000  1044  =  U  for  Hydrogen  =  Constant 


=-     UR  =0.000278=^ 
M  ,  obOU 

h=M,R=26.5957 


=  Constant. 


SCIENTIFIC  THEISM 

TABLE  III 
Atomic  Mass  Moduli  in  C.G.S.  Electrostatic  Units 


251 


c 

M 

u'   Moduli 

r>V 

R 

r'  Moduli 
,     (1.08X10")# 

Elements. 

Valences. 

Atomic 
Masses. 

(3X109) 

Atomic   Mass 
Moduli  u' 
In  C.G.S.  Units 
(Electrostatic). 

Ampere  «= 
Hours 
per  Gram 
per  Unit 
Valence. 

r 

Atomic  Mass 
Moduli  r' 
in  C.G.3.  Units 
(Electrostatic). 

Electron 

1 

1 

1  886X10  —  1S 

49069  06 

5  29946X10" 

1845 

Hydrogen 

1 

1.000 

3.48X10—" 

26.5957 

287.23356X10" 

Carbon 

4 

11.91 

41.33X10—" 

8.9606 

24.19308X10" 

Nitrogen 

3 

13.93 

48.40X10—" 

5.7405 

20.6658X10" 

Oxygen 

2 

15.88 

55.26X10-" 

3.3512 

18.09648X10" 

Sodium 

1 

22.88 

79.60X10—" 

1.1632 

12.56256X10" 

Potassium 

1 

38.86 

135.06X10—" 

0.6855 

7.4034X10" 

Iron 

2 

55.5 

193.46X10-" 

0.9576 

5.17104X10" 

Copper 

1 

63.1 

219.53X10-" 

0.4218 

4.55544X10" 

Silver 

1 

107.12 

372.66X10-" 

0.2485 

2.6838X10" 

Platinum 

2 

193.3 

672.93X10—" 

0.2752 

1.48608X10" 

Lead 

2 

205.35 

714.53X10-" 

0.2592 

1.39968X10" 

252 


SCIENTIFIC  THEISM 
TABLE  IV 


The  Masses  of  Atoms  Developed  from  the  Charge  e  and 
the  Moduli  r.  Electrophysical  Constants 


Elements. 

M. 

Atomic 
Masses. 

m 

e 
r'  ' 

Vlasses  of  Atoms. 
(Gram). 

Constanta. 

1 

9A/1Q1  vm  —  ** 

1—  Coulomb  =»  3  X109  C.G.S 
Electrostatic  Unite. 
1  —  Ampere  Hour  = 
3600  Coulombs. 
1  —  Ampere  Hour  =3600 
(3  X10»)=  1.08X10" 
(C.G.S.  Electrostatic  Unite). 

1845 

Hydrogen 

1.000 

1.662X10-" 

Constants  l 

Carbon 

11.91 

1.9731X10—" 

e,  —,N',  k',  N,  and  h. 

Nitrogen 

13.93 

2.  3100X10-" 

Electron    Charge,    e-  4.  7738 

Vlfl  —  10      mr' 

Oxygen 

15.88 

2.  6379X10-" 

(Electrostatic  Unite). 

Sodium 

22.88 

3.  8000X10-" 

(Electromagnetic   Unite). 

Potassium 

38.86 

6.4452X10—  " 

—  =  1.7664X107 
m 

Iron 

55.5 

9.  2318X10-" 

(Electromagnetic    Unite). 
=  5.2994X10" 

Copper 

63.1 

1.  0479X10-" 

(Electrostatic  Unite). 
Avogadro's  Constant, 

Silver 

107  .  12 

1.7787X10—" 

m 

Platinum 

193.3 

3.  2123X10-" 

N'-  6.  0679X10". 

Lead 

205.35 

3.4106X10—" 

k     M    3X109    3-4Sxl° 
N  =  Number       of       Electrons 
Liberated     by     1  -C.G.S. 
Electrostatic  Unit. 

N  =  k'l  =  -=2.  0938X10* 
m 

1  These  constants  were  developed  by  the  writer  from  data  given  in  this 
work. 


APPENDIX  C 

CALCULATIONS  INVOLVING  HYPERBOLIC  LOGARITHMS 

133.  Fundamental  Relations  and  Typical  Computations  In- 
volving Hyperbolic  Logarithms. 

The  reader  who  is  familiar  with  mathematical  analysis 
will  find  nothing  new  in  the  following  discussion  on  hyper- 
bolic logarithms.  This  appendix  is  intended  to  assist  those 
readers  who  are  less  familiar  with  mathematical  manipula- 
tions in  deriving  for  themselves  the  hyperbolic  relations 
which  constitute  the  physico-mathematical  foundations  of 
the  Space-Time  Potential. 

Logarithms  calculated  to  the  base  e  —  2.7182818285+ 
are  known  as  Napierian,  natural,  or  hyperbolic  logarithms, 
in  contradistinction  to  logarithms  calculated  to  the  base  10, 
which  are  called  common  logarithms.  We  will  use  the  term 
hyperbolic  logarithm  in  this  discussion  in  preference  to 
natural  or  Napierian,  because  the  fundamental  curve  per- 
taining to  our  system  is  an  hyperbola. 

Let  N  be  any  given  number.  Then  the  logarithm  of  N 
to  the  base  C  is  written  logcN  and  the  logarithm  of  N  to 
the  base  e  is  written  loge  N. 

The  following  fundamental  equations  hold  good  : 

logcNn  =  n.logcN  .................................  (28). 

If  N  =  Cy,  then  y  =  logcN  ..............................  (29). 

Using  any  other  base  as  e,  we  have 

logeN  =  loge(C?  -y.log.C  .............................  (30). 

because  N  =  Cy.     Now  since  y  =  log0N,  we  have 

logeN  =  logcN(logeC)  .........................  .........  (31). 

Now,  if  N  =  e,  and  knowing  that  logNN  =  1,  Equation  31  becomes 

logNN  =  logcN(logNC),  which  gives 

l=logcN(logNC),  or  logNC=i^  ......................  (32). 

From  Equation  31  it  follows  that 


253 


254  SCIENTIFIC  THEISM 


But  from  Equation  32,  :  -  j^  =  logce,  and,  therefore, 


Now,  if  C  be  the  base  10.  of  the  common  or  Briggs  logarithms, 
and  e  be  the  base  2  .  7182818+  of  the  hyperbolic  system,  Equation 
34  becomes 


Consequently,  logioN  =  logioe(logeN)  ....................  (36), 

...................................  (37)- 


From  Equation  32  we  have  the  following  relations  : 

aDd  Iog-10=        .......................  (38)- 


Therefore  Equation  37  may  be  given  the  form 
logeN=logloN(loge10)  .............................  (39). 

Let    M  =  log10e=log10(2.  7182818)  =0.4342945  ............  (40). 


Then  Equation  36  becomes 

log10N  =  M(logeN)  =0.4342945(logeN)  ...............  (42). 

and  Equation  37  takes  the  form 

logjy--kOogi«N)-0  4342945(logi.N)  ..................  (43). 

But  since  ^7  =  z  =  2.3025851,  we  have  for  Equation  43, 
M 

logeN  =  z(logi0N)  =2.  3025851  OogioN)  ...................  (44). 

Equations  42,  43,  and  44  constitute  our  transformation  equations 
In  the  above  the  value  M  is  known  as  the  modulus  of  common 
logarithms. 

The  reciprocal  ^  of  any  number  N  is  of  importance  in  the 
Space-Time  Potential.  The  reciprocal  ^7  is  generally  given  as 
a  decimal  fraction. 

The  following  relation  is  evident: 

logel-logeN  =  0.0-logeN=  -iogeN  ..........  (45). 

Therefore, 
e=  -logeN  =  -z(logioN)  -  -2  .  302585  l(logioN)  ....  (46). 


SCIENTIFIC  THEISM  255 

In  order  to  find  the  hyperbolic  logarithm  of  a  decimal  fraction, 
place  it=Tj,  solve   for  N,  and  substitute  the  value  of  N  thus 

obtained  in  the  expression  2.  3025851  (log  ioN)  of  Equation  46. 

In  Table  I,  col.  1,  we  find  the  value  0.0000561492.  In 
order  to  illustrate  the  procedure,  we  will  calculate  the  hyperbolic 
logarithm  of  this  decimal  fraction. 

Let  1  =  0.0000561492,    then  N  =  -17809.7 


From   Equation  46,   log/|r)=  -logeN  =  -loge(17809.7) 

But  loge   17809.7  =  2.3025851(logiol7809.7),    and   since 
logio  17809.7=4.2506574,  it  follows  that 

loge  17809.7  =  2.3025851  (4.2506574).     Performing  this  multi- 
plication by  common  logarithms,  we  have 

Iogi02  .  3025851  =  0  .  3622157 

Iog104  .  2506574  =  0.6284561 
log  (Ioge17809  .  7)  =0.  9906718 

The  number  corresponding  to  the  common  logarithm  0.9906718 
is  =  9.  7875, 
which  therefore  =  loge!7809.7. 

Since  loge(  TT  )=  —  logeN,  it  follows  that 

-  9  .  7875  -  loge         =  loge  -  loge(0  .  0000561492)  . 


In  order  that  every  phase  of  these  transformations  may  be  under- 
stood we  give  the  following  illustrative  examples. 

Given  the  hyperbolic  logarithm  —2.99573,  required  the 
corresponding  number. 

Using    Equation    42,    logi0N  =  M(logeN),    we    have,    since 

-2.99573=logeQj-)=  -logeN, 

log10N  =  0  .  4342945(logeN) 

=0.4342945  (2.99573);  performing  this  multiplication 
by  common  logarithms,  we  have 
logioO  .  4342945  =  9  .  6377843  -  10 
Iogio2.  99573     =0.4765030 
log(logioN)        =0.1142873 

The  number  corresponding  to  the  common  logarithm  0.1142873 
is  1.3010300  =  logioN.  Therefore  JV,  the  reciprocal  of  the 
required  number,  is  =  20. 


256  SCIENTIFIC  THEISM 


But  -  2 . 99573  =  loge(  =r=  I,  therefore  ^  =  — 


Given  the  decimal  fraction  0  .  4,  we  find  the  hyperbolic  logarithm. 
Let  ^=0.4,  then  N=jr-r=2.5,  as  before, 

Ioge2  .5  =  2.  3025851  (Iogio2  .  5)  ; 

but  Iogi02.  5  =  0.3979400,   consequently  Ioge2.5  =  2.3025851 
(0.3979400),  and  using  common  logarithms  for  the  multiplica- 
tion, we  have 

Iogi02  .  3025851  =  0  .  3622157 

logioO  .  3979400  =  9.5998176-10 

Iog(loge2.5)      =9.9620333-10 
The  number  corresponding  to  the  common  logarithm 
9.9620333-10  is  0.91629,  which  therefore  =  loge2.5 


Since  loge(^rj=  —  log.-tf,  we  have 


The  above  examples  should  suffice  to  make  clear  the  method 
by  which  points  and  loci  in  the  Space-Time  Potential  are  cal- 
culated. 


APPENDIX  D 

THE  SECONDARY  FUNCTION  OF  THE  SPACE-TIME  POTENTIAL, 
AND  THE  ELECTRICAL  CHARGE  e 

134.  Calculation  of  the  Charge  exhibited  by  an  Electron, 
Using  the  Secondary  or  Logarithmic  Relations  of  the 
Work  Curve. 

We  shall  now  proceed  with  the  direct  attack  of  the  prob- 
lem before  us.  We  shall  make  use,  in  this  attack,  of  no 
other  than  the  well-established  laws  of  dynamics,  and  in 
particular  that  portion  of  dynamics  which  deals  with  uni- 
formly accelerated  motion  where  no  initial  velocity  is  in- 
volved. In  other  words,  we  assume  that  the  systems  which 
we  consider  are  responsive  parts  of  an  all-inclusive  unitary 
organism  whose  activities  in  all  its  parts  are  describable  in 
terms  of  the  Space-Time  Potential. 

In  this  and  many  other  respects  we  differ  from  classical 
science,  which  heretofore  has  had  no  single  relation  capable 
of  expressing  all  phenomenal  activities.  The  Space-Time 
Potential  provides  us  with  this  single  relation,  which  in- 
cludes gravitation,  electricity,  thermodynamics,  dynamics, 
and  statics  as  mere  categories  of  cosmic  interaction  evolving 
in  accordance  with  its  simple  and  universally  applicable 
laws. 

We  shall  have  occasion  to  use  the  following  relations  of 
dynamics  pertaining  to  uniformly  accelerated  motion  for 
no  initial  velocity; 


(47). 


y^_2s     v  , 

2s~t2      t  ..... 
_vt_v2_at2 
S~2"-2a~  2 


v    2s         /2s 
p  =  —  =  —  =  \  I  — . 
a     v      V  a 


(50). 

257 


258  SCIENTIFIC  THEISM 

In  the  foregoing  expressions: 
v  —  the  velocity, 
a  =  the  acceleration, 
s  =  the  distance,  and 
t  =  the  time. 

We  assume  that  the  general  expression  (V^niva)  repre- 
sents correctly  the  energy  of  any  material  system  whose 
mass  is  m  and  velocity  v.  Consequently,  if  we  let 

e  =  the  charge  (C.G.S.  electrostatic  units), 

D  =  the  potential  difference  (C.G.S.  electrostatic 
units)  of  liberation, 

m  =  the  mass  in  grams, 

v  =  the  velocity  in  centimeters  per  second, 

a  =  the  acceleration, 

E  =  the  energy  of  the  system, 

s  =  the  spatial  displacement  for  the  work  W, 

W  =  the  work  done  by  or  upon  the  system  during  the 
displacement, 

N  =  number  of  electrons  liberated  by  a  current  of 
1-C.G.S.  electrostatic  unit  at  a  difference  of  potential  D 
(C.G.S.  electrostatic  units), 
then 

E  =  W  =  f  F.ds=  i/2mv*  =  e.D (51) 

g 

Experimental  evidence  shows  that  the  ratio     —     is  inde- 
nt 

pendent  of  the  difference  of  potential.  Consequently,  for 
the  limits  within  which  m  is  practically  constant  the  magni- 
tude of  the  ultimate  value  of  D  required  to  liberate  an  elec- 
tron from  an  atomic  structure  is  a  function  of  Kt  the  num- 
ber of  electrons  constituting  the  particular  atom.  This  will 
be  true  universally  if  future  research  shall  show  that  the 
charge  e  is  always  a  constant  relative  ratio  like  the  velocity 
of  light.  The  evidence  of  modern  research  is  overwhelm- 
ingly in  favor  of  this  assumption.  If  this  be  true,  then  the 
two  fundamental  relativity  ratio  constants  of  the  physical 
universe  are,  first,  the  velocity  of  light  V,  and,  second,  the 
electric  charge  e  associated  with  the  electron.  We  may 
unify  these  two  fundamentals  into  the  single  relation: 
eV  =  constant,  thus  relating  the  charge  carried  by  an 
electron  to  the  velocity  of  light. 

The  ultimate  value  of  D,  the  liberation  difference  of 


SCIENTIFIC  THEISM  259 

potential  for  the  electron,  may  be  calculated  from  Equation 
14  if  we  assume  the  constancy  of  the  known  relativity  ratio 
e.  Any  attempt  to  deny  the  correctness  of  this  procedure 
involves  the  repudiation  of  the  correctness  of  Expression 
51,  above.  We  maintain  that  if  the  expression  holds  for  the 
macrocosm,  it  must  hold  for  its  constituent  miscrocosmic 
groups. 

From  our  relativity  standpoint  of  the  Space-Time  Poten- 
tial the  electric  charge  e  is  well  defined  by  the  expression 

_(ma)s_E_W 
D    ~D~D' 

indicating  the  complete  relativity  of  the  value  e.  As  (ma)  s 
approaches  an  infinite  value,  D  also  approaches  an  infinite 
magnitude.  From  the  viewpoint  of  the  Space-Time  Poten- 
tial, the  relativity  ratio  e  remains  a  constant  throughout 
the  variation  of  E  and  D. 

The  fact  that  the  experimental  difference  of  potential  D 
required  to  liberate  the  electron  varies  is  due  to  the  varia- 
tions in  the  conditions  which  pertain  to  the  experiment  and 
in  the  atomic  aggregates  used.  This  experimental  varia- 
tion of  D  is  equally  often  noted  for  liquid  and  gaseous  ions, 
but  this  fact  effects  neither  the  value  of  the  relativity  ratio 
e  nor  the  liberation  constant  D  which  pertains  to  the  elec- 
tronic particle. 

Consequently  we  are  justified  in  using  Expression  51 
for  the  calculation  of  the  value  D.  In  the  preceding  we  have 
found  that  e  =  4.775  XlO-10  C.G.S.  units,  and  m  — 
9.0081X10— *  gram.  This  value  of  m  corresponds  to  a  value 
of  v  =  3.0X109  centimeters  per  second.  Transforming 
Equation  51  and  substituting  the  above  values,  we  have 

0.5mvz    0.5(9. 0081  XlO-28)  (3.0  XlO9)         4C-Q 
—  4.775X10-" 

where  D  =  8.4878  is  in  the  C.G.S.  electrostatic  system  of 
units. 

We  purpose  to  develop  the  charge  e  by  &  direct  use  of 
the  Space-Time  Potential  in  order  to  show  its  applicability 
to  the  investigation  of  electrical  phenomena.  We  will  make 
use  of  Equation  51,  substituting  therein  the  now  known 
values  of  D  and  m.  Consequently  we  have 

eD  =  e  (8.4878)  =  (ma)  s (52). 


260  SCIENTIFIC  THEISM 

From  Equations  20  and  21,  we  have 

eN  =  l     and     e  =  ^; 

N 

substituting  this  value  of  e  in  Equation  51,  we  have 
r(D)  =  (ma)s,  which  gives 


XT        P  8-4878 


(ma)s     (9.008lX10-28)as 

Since  D  —  N(ma)s,  it  follows  that  D  is  that  difference 
of  potential  which  is  required  to  displace  N  electrons  show- 
ing a  charge  e  and  having  a  mass  ra  through  a  distance  s. 
Furthermore,  the  N  liberated  electrons  complete  their 
migration  over  the  distance  s  in  a  unit  of  time,  i.e.,  one  sec- 
ond. This  does  not  mean  that  the  translation  of  one  single 
electron  through  the  distance  s  will  require  a  unit  of  time  ; 
in  fact  it  will  be  shown  that  £,  the  time  of  migration  of  one 
electron,  is  equal  to  0.0000032361  second.  Be  it  remembered 
that  the  value  of  m  in  Equation  53  refers  to  one  electron. 
Before  we  can  solve  Equation  53,  we  must  evaluate  the 
acceleration  a  and  the  distance  s.  We  shall  employ  the 
Space-Time  Potential  for  this  evaluation. 

Let  us  place  the  value  D,  the  difference  of  potential,  = 
8.4878,  directly  in  the  Space-Time  Potential  as  exhibited  in 
Table  I,  Appendix  B.  This  means  that  we  regard  D  = 
8.4878  as  an  hyperbolic  logarithm.  If  n  be  the  number 
corresponding  to  the  hyperbolic  logarithm  8.4878,  we  have 
Iog10  n  =M  (loge  n)  ;  and  since  loge  n  =  8.4878,  we  have 
Iog10  n  =  0.4342945  (8.4878) 

—  3.686,2068,  for  which  logarithm 
n  =  4855.2,  which  value  is  found  in  Table  I. 

Since  s  =  (n  —  1)  ,  we  have 

s  —  4855.2  —  1.0  =  4854.2  centimeters. 

If  £  is  the  time  required  by  one  electron  to  migrate  the  dis- 
tance s,  we  have  from  Equation  50, 


v         o  X  10 

The  value  v  =  3x  109  c.  is  the  velocity  of  the  electron 
as  used  previously. 


SCIENTIFIC  THEISM  261 

From  Equation  48  we  have 

(55) 


Substituting  these  values  of  a  and  s  and  using  m  as 
9.0081  XlO-28  in  Equation  53,  we  obtain 

D  8.4878 , 

(ma)s     (9. 0081  XlO-28)  (9. 2703  XlO14)  (4854. 2) " 
N  =  2.0938xl09,  which  is  identical  with  the  value  of  N 
previously  obtained  (see  Equation  19). 

Consequently  it  follows  that  since 

e  —  -jj,  e  =  4.775 XlO-10  C.G.S.  electrostatic  unit,  which 

agrees  with  the  previously  calculated  value  of  e,  as  it  must, 
by  virtue  of  the  fact  that  the  value  obtained  for  N  by  the 
two  different  methods  is  identical.  Consequently  we  have 
shown  conclusively  that  the  Space-Time  Potential  is  capable 
of  deriving  directly  the  value  e, 

.135.    Fundamental    Physico-mathematical    Relations   of   the 
Space-Time  Potential. 

The  fundamental  relations  which  inhere  in  the  nature  of 
the  Space-Time  Potential  will  now  be  considered. 

Let 

TPn  =  work  done  from  point  n  to  change  point  1, 

W,t  =work  done  from  point  -  to  change  point  1, 

n 

/B=tirne  of  translation  through  distance  sn, 

t^  =time  of  translation  through  distance  S£, 

n  —  number  whose  hyperbolic  logarithm  is  Wn, 

Wn= W*  ;   tn=t* (57). 

..(58). 


(1  \      /   i 
1-nj  =  -E- 


^=^ii =n (59). 

84     (n-1) 

n 
te. 

Y£=£L  =?E=n  .  (60). 

V4     2s4     84 


262  SCIENTIFIC  THEISM 

Equation  60  is  evidently  true  because  tn  =  ti. 
J^B 

*=.«&£-?=  -n  ..(61). 

a*      2s  j     si 


Wn-(mnan)sn;  W*  =  (01^4)54  ....................  (62). 

m  4  (a  &s  4) 


1 
-ifT-  =  1  7         v      ............................... 

Wn  mn(ansn) 

nXn)^.  .......................  (64). 


m4=n2(mn);   mn  =        .............................  (65). 

For  values  of  n  <  1.11-;.    (point  /)  and  for  values  of  —  > 

0.90  (point  -j),  see  Table  I,  continued. 

The  following  facts  and  relations  are  noteworthy  : 

sn  =  s4  ...........................................  (66). 

Wn  =  W4;  tn  =  t*;  sn=(n-l);s4  =  ^^,...(57  and  58). 

From  Equation  66  we  have 

a 

—  =  n'  =  l.     Equations  60  to  65,  inclusive,  take  the  form: 
s* 

vn  _an  _mp  _  mnan 
v*     a*     m* 


Wn  .  R. 

1  ....... 


vn  =  VA;  an=a*;  mn  =  m4;  (mnan)  =  (m^a*)  .........  (69). 

Since  sn  =  (n  —  1),  and  54  =(l  --  j;  sn  =  S4, 


It  follows  that 

and 


Equations  66  to  70,  inclusive,  pertain  to  the  microcosm,  with 

n<l.llj  and  ->0.90 
9  n 

The  above  developed  relations  are  found  partially  exem- 
plified in  Table  I,  and  they  serve  for  the  calculation  of  the 
fundamental  elements  of  the  Space-Time  Potential. 


SCIENTIFIC  THEISM  263 

136.     The  Macrocosm  and  the  Microcosm. 

The  Space-Time  Potential  differentiates  itself  into  two 
systems  having  distinctive  properties.  The  first  system  is 
obedient  to  the  dictates  expressed  by  Equations  57  to  65, 
inclusive,  and  the  second  system  is  submissive  to  the  man- 
dates of  Equations  66  to  70,  inclusive.  In  the  first  system 
s»  does  not  equal  s+;  in  the  second  system  sn  equals  s*. 

The  first  system,  that  of  unequal  radii  (s»  =£  Sn)  is 
represented  in  Fig.  27  and  Table  I,  Appendix  B.  The  first 
system  is  the  macrocosmic  system,  the  great  world  of  mole- 
cules, bodies  and  planets.  The  second  system  is  the  micro- 
cosmic  system,  the  small  world  of  "positons,"  "energons," 
electrons,  and  atoms.  The  second  system  is  that  of  equal 
radii  (SB  =  st)  with  the  positive  loci  continuous  with  the 
corresponding  negative  loci.  The  change  point  bisects  the 
vectorial  distance  between  positive  and  negative  loci  of  equal 
magnitude  in  the  microcosm.  This  the  change  point  does 
not  do  in  the  macrocosm.  Some  phases  of  the  microcosm 
are  shown  in  Table  I,  Continued,  Appendix  B.  A  rotary 

system  corresponding  to  n  =  x  and  —  =  —  in  Table  I,  Con- 
tinued, is  in  dynamic  equilibrium  and  constitutes  an  ele- 
mentary type  of  activity  structure.  We  give  to  this  elemen- 
tary type  of  microcosmic  structure  the  name  "energon." 
From  the  standpoint  of  the  Space-Time  Potential,  the  ener- 
gon is  a  unit  composed  of  positive  and  negative  work  fac- 
tors of  equal  magnitude,  eternally  inseparable  in  the  world 
of  phenomenal  interaction.  Those  mysterious  antipodal 
activities,  known  as  attraction  and  repulsion,  no  longer  re- 
main enigmatical  and  unintelligible.  Gravitational  attrac- 
tions and  electrical  repulsions  are  but  phases  of  interaction 
in  the  Space-Time  Potential.  The  positive  work  factors  of 
the  energon  is  the  basis  of  the  so-called  positive  nucleus  of 
the  modern  electronic  theory.  It  no  longer  remains  the 
elusive  mystery  of  the  electronic  hypothesis,  but  becomes 
the  well-defined  complement  in  a  structure  typical  of  all 
microcosmic  and  macrososmic  structures. 


APPENDIX  E 

ELECTROLYTIC  IONIZATION— THE  KAUFMANN  EFFECT— THE 
RELATION  OF  WORK  Loci  TO  THE  ATOMIC  STRUCTURE 
AND  DIAMETER — AVOGADRO'S  CONSTANT — THE  SPACE-TIME 
POTENTIAL  THEORY  OF  LIGHT  SUBSTANTIATED  BY  RECENT 
ASTRONOMICAL  OBSERVATIONS 

137.  Electrolytic  lonization  According  to  the  Space-Time  Po- 
tential. 

The  Space-Time  Potential  enables  us  to  comprehend  the 
action  in  an  electrolytic  cell.  Consider  the  rotary  molecular 
system  a-b  of  Fig.  31,  existing  in  dynamic  equilibrium.  Let 
the  solute  system  a-b  be  immersed  in  the  solvent  component 
c-d  of  the  electrolytic  cell  A-B,  a-b,  c-d,  shown  in  Fig.  34. 
The  displacements  of  the  solvent  molecules  of  the  system 
c-d  by  the  solute  molecules  a-b  results  in  a  readjustment  of 
work  loci  in  a  manner  tending  toward  the  restoration  of 
equilibrium  in  the  combined  system  A-B,  a-b,  c-d.  Being 
a  different  molecular  structure,  the  solvent  system  c-d  dif- 
fers in  the  configuration  of  its  work  loci  from  the  solute 
system  a-b,  consequently  the  unbalanced  potential  differ- 
ences initiated  at  immersion  strive  at  once  for  a  readjust- 
ment tending  toward  equilibrium. 

The  modified  system  a-b  plus  the  modified  system  c-d 
constitutes  the  electrolyte  of  the  cell  shown  in  Fig.  34.  Let 
us  now  subject  the  combined  system  to  an  increasing  differ- 
ence of  potential.  The  modified  system  a-b  is  considered  as 
existing  in  a  state  of  rotation  about  its  change  point  at  the 
time  when  a  potential  difference  is  impressed  upon  the  cell 
system.  The  increasing  potential  difference  exerts  a  damp- 
ing influence  upon  the  rotary  system  a-b.  The  angular  velo- 
city decreases  with  an  increase  in  the  potential  difference 
until  it  becomes  equal  to  zero  at  the  time  when  the  decom- 
position voltage  (B-A)  =D  has  been  reached.  Simultaneously 
with  this  damping  effect,  the  system  a-b  is  displaced  so  that 

264 


SCIENTIFIC  THEISM  265 

its  change  point  becomes  coincident  with  the  mobile  re- 
sultant change  point  of  the  entire  cell  system.  At  the  time 
when  angular  accelerations  have  become  equal  to  zero,  then 
linear  accelerations  are  given  to  the  systems  a  and  b  along 
the  work  line  c  w.  Since  the  potential  at  w  is  not  equal  to 
the  potential  at  c,  it  follows  that  the  mobile  factors  in  the 
cell  must  move  continuously  while  a  difference  of  potential 
between  A  and  B  is  maintained.  The  mobile  portions  of  the 
cell  system  strive  to  neutralize  the  potential  difference  be- 
tween A  and  B.  As  the  resultant  change  point  4  moves 
toward  B,  the  change  point  3  of  the  system  b-B  precedes  it 
and  should  arrive  at  B  in  advance  of  point  4-  The  system  6 
must  increase,  for  the  distance  C-3  approaches  zero  more 
rapidly  than  the  distance  b-3,  which  also  tends  toward  zero. 
Simultaneously  with  the  beginning  of  an  increase  in  the 
system  b,  we  must  have  a  decrease  in  the  system  a  accom- 
panied by  a  retrograde  motion  of  a.  Fig.  36  shows  the  work 
relations  which  obtain  to  the  system.  The  increment  of 
work  -{-ed  is  equal  to  the  decrement  of  work  — ed.  Obser- 
vations in  which  these  positive  and  negative  work  factors 
are  clearly  manifest  are  responsible  for  the  creation  of  that 
interdependent  action  phase  entity  which  is  known  as  the 
charge.  The  fact  is  that  the  charge,  regarded  as  a  separate 
independent  entity,  does  not  exist.  Work  increments  and 
decrements  are  the  given  data  of  experience;  charges  are 
conceptual  conveniences  resorted  to  in  physico-mathematics. 
The  work  increment  -f  ed  appears  at  the  electrode  c,  and 
simultaneously  the  work  decrement  — ed  is  found  at  the 
electrode  w.  The  algebraic  sum  of  the  work  done  within 
the  cell  is  zero. 

The  Hittorf  experiments  no  longer  remain  subject  to  the 
guesses  of  an  "extraordinary  hypothesis,"  but  follow  as 
consequences  from  the  Space-Time  Potential.  In  fact,  none 
of  the  herinbefore  enumerated  objections  to  the  ionic 
hypothesis  remain  as  such  for  the  relations  pertaining  to 
the  Space-Time  Potential, 


266 


SCIENTIFIC  THEISM 


I  i  'point 
I  '  J 

Dierence  in  Potential '*  &'- 
| !  i 


of  ftectrotysts . 


SCIENTIFIC  THEISM  267 

The  scope  of  the  present  discussion  makes  it  impossible 
to  give  further  consideration  to  this  phase  of  the  subject, 
which,  we  realize,  has  been  merely  touched  upon  en  passant, 
without  in  any  way  doing  it  justice.  That  part  of  our  dis- 
cussion which  pertains  to  the  phenomenon  of  electrolysis 
must  therefore  be  regarded  as  suggestive  rather  than  re- 
plete with  detail. 

138.    The  Kaufmann  Effect. 

When  a  mass-acceleration  kern  or  center  passes  suc- 
cessive work  loci,  the  kern  must  obey  the  mandates  of  each 
consecutive  locus  and  assume  the  mass-acceleration  magni- 
tude which  pertains  to  the  particular  locus  at  which  it  may 
be  found  during  its  migration. 

If  the  space  s  traversed  in  a  unit  of  time  be  related  to 
the  distance  K,  the  Kosmometer  =  3xl010  centimeters; 
then  we  have  from  the  fundamental  relations  of  the  Space- 
Time  Potential ; 


and 


V 

This  expression,  evolved  from  our  system  of  relative 
physical  interaction  and  interdependence,  describes  mathe- 
matically the  variation  of  the  kern  magnitude  with  the 
variation  in  velocity. 

In  Table  V  the  values  derived  from  the  expression  of 
Lorentz-Einstein  and  the  writer  are  compared  with  the 
observed  values  of  Kaufmann. 


268 


V 

V" 

Lorentz- 
Einstein. 

H)T 

Reuterdahl. 

io?eji-jd 

Kaufmann. 
(Observed). 

V 

T 

0.75 

1.512 

1.8391 

1.65 

0.78 

1.598 

1.9315 

1.83 

0.80 

1.667 

2.000 

1.88 

0.83 

1.793 

2.1242 

2.09 

0.86 

1.960 

2.2748 

2.43 

0.88 

2.105 

2.3974 

2.73 

0.90 

2.294 

2.5472 

3.09 

139.     The  Relation  of  Work  Loci  to  the  Atomic  Structure  and 

Diameter. 

From  Table  I,  Continued  (Appendix  B),  we  may  de- 
rive our  basic  ideas  concerning  the  structure  of  the  atom. 
The  work  loci  shown  in  this  table  constitute  the  orbits  for 
the  sub-atomic  particles.  We  have  previously  stated  that 
the  sub-atomic  particles  are  capable  of  variation  in  an  as- 
cending and  a  descending  manner  from  a  neutral  state — 
the  energon.  The  orbits  in  the  case  of  atoms  are  circular 
concentric  work  loci.  The  radial  distances  of  the  orbits  are 
functions  which  depend  upon  the  system  and  the  funda- 
mental relations  of  the  Space-Time  Potential  for  their 
magnitude.  If  work  is  done  upon  or  by  the  system,  the 
components  thereof  undergo  corresponding  changes.  The 
work  loci  configurations  are  modified  to  conform  with  the 
involved  work  factor.  When  an  energon  is  caused  to 
migrate  from  one  work  locus  or  orbit  to  another,  it  assumes 
that  magniude  which  conforms  with  the  work  constant  of 
the  orbit  upon  which  it  becomes  located.  An  energon 
located  upon  the  outermost  orbit  of  the  atom  is  an  electron. 
Passing  inward  toward  the  center,  we  find  energons  in 
various  loci  phases  until  we  reach  the  limit  of  variation  in 


SCIENTIFIC  THEISM  269 

the  positon.  We  find,  in  fact,  variations  in  the  energonic 
condition  which  not  only  suggest  the  spectrum,  but  make  it 
possible.  Millikan  makes  the  following  statement  concern- 
ing the  justly  famous  Bohr  atom:  "Its  chief  difficulty 
arises  from  the  apparent  contradiction  involved  in  a  non- 
radiating  electronic  orbit  —  a  contradiction  which  would 
disappear,  however,  if  the  negative  electron  itself,  when 
inside  the  atom,  were  a  ring  of  some  sort  capable  of  ex- 
panding to  various  radii,  and  capable,  only  when  freed 
from  the  atom,  of  assuming  essentially  the  properties  of  a 
point  charge,  such  as  we  find  it  endowed  with  in  experi- 
ments upon  cathode  rays,  /3-rays,  and  ionization  in  gases."1 
Millikan  keenly  realizes  that  a  fixed  primordial  particle 
is  incapable  of  explaining  the  phenomena  in  question.  In 
this  work  we  have  repeatedly  pointed  out  the  necessity  of 
variability  in  the  primordial  particle  in  conformity  with 
the  requirements  of  our  universal  relativity  system.  It  is 
evident  that  the  atom  of  the  Space-Time  Potential  obviates 
entirely  the  difficulties  encountered  in  the  Bohr  atom.  It 
is  also  clear  that  the  diameter  of  an  atom  cannot  be  re- 
garded as  an  absolutely  fixed  quantum.  Whenever  we 
speak  of  the  diameter  of  an  atom,  therefore,  we  must  de- 
fine the  conditions  imposed  upon  the  system.  By  defining 
a  normal  condition  we  would  be  in  a  position  to  evaluate 
the  corresponding  diameter,  which  then  would  constitute 
the  normal  value. 

140.     Avogadro's  Constant. 

Table  IV,  Appendix  B,  affords  the  required  data  for 
the  computation  of  Avogadro's  Constant.  The  following 
relations  are  involved  in  the  calculation  : 

R  =  ampere-hours  per  gram  per  unit  valence, 

(1.08xl013)R,  „„  o     i 
r'  —  -^  C.G.S.  electrostatic  units, 

v 
e 
m  =  —  r  =  actual  mass  of  atom  in  grams, 

M  =  atomic  mass  of  atom  (ratios  with  hydrogen  =  1.0) 


m 


1  Robert  A.  Millikan,  The  Electron,  p.  216. 


270  SCIENTIFIC  THEISM 

The  results  of  the  calculations  are  given  in  Table  VI. 

TABLE  VI 
Avogardo's  Constant 


Elements. 

AT-M. 
m 

Hydrogen 

6.01685X10" 

Carbon 

6.03596X10" 

Nitrogen 

6.03027X10" 

Oxygen 

6.01975X10" 

Sodium 

6.02100X10" 

Potassium 

6.02931X10" 

Iron 

6.01180X10" 

Copper 

6.02134X10" 

Silver 

6.02219X10" 

Platinum 

6.01800X10" 

Lead 

6.02084X10" 

Average  value 
of  AT'  

.6  022482X10" 

For  Hydroger 

i  Af  =  1.000 

Transforming  this  average  value  of  N'  based  upon  Hydro- 
gen M  =  1.000  to  the  Oxygen  Standard  M  =  16,  we  have 

16.00 

AT  =.nr5o-  (6.022482X1023)  =  6.0679X1023. 
lo.oo 

141.    The  Space-Time  Potential  Theory  of  Light  Substan- 
tiated by  Recent  Astronomical  Observations. 
At  the  time  when  the  fundamental  concepts  of  the 
Space-Time  Potential  were  developed,  the  writer  was  con- 
fident that  future  investigations  in  the  field  of  physical 
astronomy  would  bring  forth  facts  substantiating  that  por- 
tion of  his  work  which  dealt  with  the  phenomenon  of  light 


SCIENTIFIC  THEISM  271 

as  a  particular  case  of  universal  interaction  between  mate- 
rial particles.  The  reader  is  referred  to  paragraph  76 
(Fields  of  Interaction)  and  paragraph  86  (Primary  and 
Secondary  Matter  in  the  Role  of  Concurrent  and  Excitant 
Systems) .  From  these  paragraphs  and  many  other  similar 
statements  in  the  text  it  is  evident  that  we  regard  light  as 
a  case  of  interaction  between  material  particles.  The  path 
of  an  excitant  particle  in  an  interacting  field  like  the  sun's 
is  then  determined  by  the  conditions  set  forth  in  paragraph 
76.  The  path  of  propagation  of  an  excitant  light  particle 
must  sustain  deviation  whenever  the  particle  passes  a  body 
like  the  sun.  The  observations  made  of  the  total  solar 
eclipse  (May,  1919)  prove  conclusively  that  the  path  of 
propagation  of  light  emanating  from  a  star  is  deviated 
from  its  previously  assumed  rectilinear  path  when  it  passes 
near  the  sun. 

This  astounding  discovery  proves: 

1.  That  light  is  a  material  and  not  an  etherial 
phenomenon. 

2.    That  the  ether  medium  is  not  a  physical  reality,  but 
merely  a  mathematical  myth. 

3.  That  the  laws  of  the  primordial  particle   (micro- 
cosm) are  the  laws  of  the  universe  (macrocosm) . 

4.  That  interdependence  is  universal  in  the  unitary 
interacting  system  called  the  cosmos. 

The  writer  first  held  these  views  in  the  year  1896.  The 
first  published  intimation  of  these  conclusions  appeared  in 
Volume  I,  No.  1,  of  the  Transactions  of  the  American  Elec- 
trochemical Society,  April  5,  1902,  under  the  title  "The 
Atom  of  Electrochemistry." 

The  amount  of  the  deflection  of  light  may  be  easily  cal- 
culated without  recourse  to  speculations  concerning  the 
fourth  dimension  and  without  the  use  of  the  theory  of 
invariants. 

Consider  the  system  composed  of  an  excitant  particle 
of  mass  ra  and  the  sun  of  mass  M.  Since  ra  is  small  com- 
pared with  M  the  center  of  gravity  of  the  system  may  be 
regarded  as  coincident  with  the  sun's  center.  Locate  the 
combined  mass  (M-f  m)  =  M  (since  m  is  small)  at  this 
center  of  gravity.  The  sun's  radius  R  will  constitute  the 


272  SCIENTIFIC  THEISM 

distance  of  nearest  approach  of  the  particle  m  moving  along 
its  hyperbolic  path  into  the  sun's  field  of  interaction. 
Let, 

t  =  transverse  axis  of  the  hyperbola. 
V  =  average  velocity  of  the  excitant  particle  m.    The 
upper  limit  of  v  =  V    (the  velocity  of  light) 
=  S.OxlO10  cms.  per  sec.     The  lower  limit  for 
excitation  is  taken  at  1010  cms.  per  sec.    The  aver- 
age value  of  v  —  2.0  xlO10  cms.  per  sec. 
Vi  =  transverse  velocity. 
v»  =  initial  relative  velocity  of  m  and  M. 
R  =  distance  of  nearest  approach  of  m  to  M  =  6.95552 

XlO10  cms. 

Y  =  constant  of  interaction. 
6  =  the  deflection. 

I  =  interactional  intensity ;  is  a  function  of  the  inverse 
first  power  of  the  distance  and  the  potential; 
I  =  (27.64x981)  =  27,115  dynes. 
Then  the  following  relations  may  be  derived  easily : 
M  M 

V     /1t -.    , v—    V2     —     V2  •    t     ^^     .,-..,    , r-       XV     '=•     XV  ', 

(M-f-m)  (M-fm) 

v_v0=2Av       2A         2A 


tv2        tv       ~  Rv 
where  A=  Y  (M-j-m)  =  Y  M  (since  m  is  small)  =  I  (R) 2 ; 

I  =  27,115  dynes ;  A  =  I  (R) 2  =  27,115  (6.95552  x  1010) 2 
=  1.3118  xlO26; 

2A_  2  (1.3118  x  1026) 

vi  =       Rv  :  :   6.95552  x  1010  (2.0  x  1010)   :     ^88599  x  10* 

v,       1.88599  x  105 
tan  0  =  ^-  =     2  0  x  1Q10     =  9.42995-';  6  -  1.95". 

The  observed  deflection  9  was  calculated  from  the  data 
secured  by  the  English  Solar  Expedition  on  May  29,  1919. 
Sir  Frank  Dyson  states :  "But  the  much  better  plates  gave 
for  the  displacement  at  the  limb  1.98"— Einstein's  predicted 
value  being  1.75"."  (See  "The  Reflection  of  Light  by  Gravi- 
tation and  The  Einstein  Theory  of  Relativity,"  in  the 
Scientific  Monthly  for  January,  1920,  page  81.) 


APPENDIX  F 

INTERDEPENDENT  AND  INDEPENDENT  MOTION.    THE  INTER- 
ACTION COEFFICIENTS.    SOME  BASIC  FALLACIES 
OF  PARTIAL  RELATIVITY 

142.    Interdependent  and  Independent  Motion. 

The  old  notions  of  algebraic  additivity  of  velocities  still 
hold  despite  the  fallacious  interpretations  put  upon  these 
relations  by  the  partial  relativists.  The  great  service  which 
the  partial  relativists  have  rendered  to  intellectual  progress 
consists  in  their  splendid  and  persistent  insistence  upon  the 
general  principle  of  relativity.  It  is  regrettable,  indeed,  that 
they  have  grossly  misinterpreted  the  meaning  of  their  own 
results.  They  have  failed  to  distinguish  correctly  between 
interdependent  motion  and  independent  motion  just  as  they 
have  failed  to  distinguish  between  real  space  and  mathe- 
matical space. 

Absolutely  independent  motion  is  purely  theoretical  but 
it  may  be  described  in  terms  of  formal  space  and  time.  In- 
dependent motion  is  closely  simulated  by  two  bodies  moving 
under  independent  locomotion  intensities.  The  analysis  of 
independent  motion  resolves  itself  into  a  pure  mathematical 
investigation  involving  the  space  and  time  forms.  When  we 
deal  with  actual  physical  motion  we  are  confronted  with 
interdependent  interaction  resultants  that  can  be  described, 
in  part,  in  terms  of  the  forms  of  space  and  time  but  which 
involve  activity  factors  which  transform  and  modify  the 
merely  formal  results  of  a  purely  mathematical  analysis 
into  cases  of  genuine  physical  activity  vectorials.  These 
physical  activity  vectorials  may  be  redescribed  in  terms  of 
the  pure  forms  of  space  and  time  but  the  redescription  must 
take  account  of  the  effects  of  the  interdependent  factors  of 
interaction. 

273 


274  SCIENTIFIC  THEISM 

The  Principle  of  Algebraic  Additivity  holds  for  velocities 
pertaining  to  theoretical  independent  motion.    Thus  if, 
vx  =  velocity  of  particle  1, 
v,  =  velocity  of  particle  2,  and 
vr  =  relative  velocity  of  particles  1  and  2,  then 
a    For  Motions  in  the  Same  Directions, 

vr   =  vt  —  va. 
b    For  Motions  in  the  Opposite  Directions, 

V,     =    Vj    +    V2. 

143.     Interdependent  Motion  as  Exemplified  in  the  Phenom- 

enon of  Light. 

For  the  relations  and  magnitudes  of  the  involved  veloc- 
ities the  reader  is  referred  to  Paragraph  108.  We  regard 
the  velocity  of  light  V  as  a  constant  ratio  obtained  by  divid- 
ing the  velocity  of  the  excitant  system  vn  by  the  velocity  of 
the  concurrent  system  VA. 

From  Paragraph  108  we  have, 
V  =  relative  velocity  =  —  S-=  velocity  of  light, 

*  n 

vff  =   (V—  1)  ;  and  VA  =(-i. 


According  to  the  Principle  of  Algebraic  Additivity, 
V  (the  relative  velocity)  should  equal  (vtf  -(-  VA). 
When  we  substitute  the  known  values  of  v»  and  VA,  however, 
we  find; 

(V—  1)      (V°—  1) 


(vn  +  VA)  =  (V— 1)  + 


V 


(V2 l) 

Be  it  noted  that,  = — —A  is  less  than  V.    This  proves 

conclusively  that  a  direct  application  of  the  Principle  of 
Algebraic  Additivity  apparently  fails  in  the  case  of  Inter- 
dependent Motion.  This  failure  is  due  to  the  introduction  of 
genuine  activity  factors  which  produce  a  new  configuration 
in  the  original  theoretical  system.  Vectorial  resultants  of 
interaction  have  been  produced  and  it  is  futile  to  expect  them 
to  have  the  same  magnitudes  as  the  factors  in  the  purely 
theoretical  system.  Therefore  we  cannot  expect  these  trans- 
formed factors  of  interaction  to  conform  with  the  Principle 
of  Algebraic  Additivity  unless  we  allow  for  the  magnitude 


SCIENTIFIC  THEISM  275 

of  the  transformation.  Be  it  noted,  however,  that  the  Prin- 
ciple of  Algebraic  Additivity  is  applicable  to  the  actual,  true 
magnitudes  of  the  vectorial  resultants.  The  apparent  fail- 
ure of  this  Principle  is  due  therefore  to  a  misinterpretation 
of  physical  facts  and  a  consequent  misapplication  of  the 
Principle. 

144.    Independent  Motion.    The  Additivity  Principle  and  the 
Velocity  of  Light. 

We  have  seen  in  the  preceding  paragraph  that  it  is  in- 
correct to  apply  the  Principle  of  Algebraic  Additivity  to  the 
interaction  factors  involved  in  the  phenomenon  of  light  un- 
less we  make  due  allowance  for  a  genuine  physical  trans- 
formation due  to  interaction.  We  shall  now  investigate  the 
requirements  of  the  Additivity  Principle  in  the  case  of  the 
phenomenon  of  light. 
Let, 

Ve  =  the  velocity  of  the  excitant  system  operating 

under  the  Principle  of  Additivity, 
vc  =  the  velocity  of  the  concurrent  system  actuat- 
ing under  this  same  Principle, 

V    —  relative  velocity  =—  —  =  velocity  of  light. 

v« 

In  order  that  the  relations  may  conform  with  the  require- 
ments of  the  Principle  of  Additivity  we  must  have, 
V2  V 

Ve=(V+l)  Vc- 


The  Principle  of  Additivity  for  motions  in  opposite  direc- 
tions as  in  the  present  case  requires  that, 

V  =  v,+  vc. 

Substituting  the  previous  values  of  v,  and  vc  in  the 
above  relations  we  obtain, 

_,  V2  V  V(V+D    =v 

:V*        V°-  " 


(v+ir  (v+i) 

Moreover,  these  values  of  ve  and  vc   satisfy  the  re- 
quirement that, 

V2 


(V+D 


276  SCIENTIFIC  THEISM 

We  cannot  expect  that  these  values  of  ve  and  vc  shall  be 
equal  respectively  to  the  values  of  vn  and  v*  given  in  Para- 
graph 143  because  they  do  not  refer  to  the  same  magnitudes. 
The  values  vc  and  vc  refer  to  simple  independent  theoret- 
ical motion.  The  values  vn  and  vt  refer  to  vectorial  inter- 
action resultants  due  to  the  simultaneous  interaction  of 
transverse  and  longitudinal  activity  factors.  Therefore 
there  is  no  real  discrepancy  in  the  respective  values  because 
they  do  not  refer  to  the  same  factors. 

Consequently  it  is  a  gross  fallacy  to  attempt  to  place  the 
blame  for  this  apparent  discrepancy  upon  a  fictitious  four 
or  n  —  dimensional  manifold.  The  mathematical  legerde- 
main of  the  four-dimensional  conjurors  is  interesting  and 
exciting  but  it  is  a  colossal  fallacy  to  try  to  force  real 
physical  phenomena  into  the  phantasmagoria  of  a  non-exist- 
ent, unreal  hypothetical  space. 

145.    The  Interaction  Coefficient  in  the  Case  of  Light. 

The  relations  between  interdependent  and  independent 
motion  may  be  expressed  as  coefficients  to  which  we  give  the 
name  "Interaction  Coefficients."  The  Interaction  Coefficient 
J^  for  Light  may  be  derived  from  the  expressions  given  in 
Paragraphs  143  and  144  as  follows  : 
V2—  1 


T      .     « 

L  "  ve  +  ve  V 


V  (V2-D  - 


(V— 1)  (V2— 1) 

IL  =  _»     =     


v^ 
v. 


. 

v 


1 

h_    _ 

e 

V2 

V2 
(V2—  1) 

(V+l) 
(V—  1) 

V 

(V+l) 

x?-° 

1 

V1 

•(•-*> 

-(•--V> 

-    ('  -  4r) 


In  this  form  we  recognize  our  Interaction  Coefficient  as 
the  Fundamental  Scalar  of  the  Einstein  Relativity  for  the 
case  of  a  unit  velocity  and  the  velocity  V. 


SCIENTIFIC  THEISM  277 

The  Genital  Number  n  and  the  Interaction  Coefficient 
/    are  related  as  follows  : 


;  n  =  V,  therefore 

and 


= 


n 

For  ordinary  interacting  and  interdependent  systems  the 
involved  velocities  will  be  small  in  comparison  with  the 
velocity  of  light.  The  preceding  discussion  refers  to  the 
maximum  condition  which  pertains  to  the  velocity  of  light. 
It  follows  that  the  genital  numbers  in  the  case  of  the  Inter- 
action Coefficient  7L  for  light  are  V  and  1;  that  is,  in  the 
secondary  or  logarithmic  function  we  have  included  the 
Change  Point  (See  Table  I,  Appendix-B). 

In  the  case  of  the  General  Interaction  Coefficient  7G 
the  genital  numbers  of  the  system  may  be  in  general,  desig- 
nated as  n  and  a.  In  that  case  7G  becomes  identical  with 
IL  when  n  reaches  its  maximum  value  V  and  a  reaches  its 
minimum  value,  that  is,  unity.  The  unit  of  measurement 
employed  may  readily  be  so  chosen  that  a  =  1  in  the  limiting 
case. 

For  the  general  case  with  the  Interaction  Coefficient  = 
/G  we  see  that  : 

n  <  V,  n  >  a,  and  a  >  1. 
In  the  limiting  case  when  IQ  =  IL,  we  have: 
n  =  V  and,  a  =  1. 

146.     General  Case  of  Interdependent  Motion, 

The  genital  numbers  n  and  a  are  related  to  the  velocities 
vn  and  v*  by  the  following  expressions  : 

I          1  \          (n—  a) 
-~ 


v= 


v* 

an 


278  SCIENTIFIC  THEISM 

These  relations  follow  as  consequents  from  the  Funda- 
mental Relations  of  the  Space-Time  Potential.  See  Para- 
graphs 135  and  143. 

147.     General  Case  of  Independent  Motion. 

It  is  clear  from  an  inspection  of  the  above  in  conjunction 
with  Paragraph  144  that  for  the  genital  numbers  n  and  a, 
the  velocities  ve  and  ve  are  given  by  the  following  ex- 
pressions : 

n2  n 

V"^  -^___^_^___  •         V       — 

e  »        vo 


(n  +  a)  a(n  +  a)  ' 

n2 


(n  +  a)     = 


n 


a(n  +  a) 
(v    +  v  )-  - 


a)  "  a(n  +  a) 


148.    General  Interaction  Coefficient. 
(n—  a)  (an  -f  1) 


T        (vg  +  v*)  __  an  _(n2—  a2)_/         a*\ 

~  (v.  +  v,)  "     n(an  +  1)  n2      ~V      'n2/' 


a(n  4-  a) 


=    Y«_    =         (n— a) 
v.  n2 


(n  +  a) 
(n^a) 


(n2— a2)         /          a2  \ 

-HZ-      v     •*;• 


Vi_     _  an          _    (n2— a2)  _ 

vc  n  n2 

a(n  -\-  a) 


a2  v 

F~*  v4 


Tn  V          "c     —    -I 

2  rr~       A         —  —  A. 


Consider  the  right  triangle  ABC  in  which  the  hypotenuse 
AB  =  ve,  EC  —  vn,  and  included  angle  at  B  =   0,  then; 


SCIENTIFIC  THEISM  279 

Similarly  for  the  right  triangle  DEF  in  which  the  hypo- 
tenuse DE  =  ve,  EF  =  vit,  and  included  angle  at  E  =  6 
then; 


Now  consider  the  right  triangle  GHI  in  which  the  hypo- 
tenuse GH  =  n,  HI  —  v  (n2-a2)  ,  IG  —  a,  and  the  angle  H 
included  between  GH  and  HI  =  d,  then  ; 


=cos  e  = 


This  is  the  Fundamental  Scalar  Relation  of  the  Einstein 
Relativity.  In  Professor  Richard  C.  Tolman's  work  entitled, 
"The  Theory  of  the  Relativity  of  Motion"  (1917),  this 
Fundamental  Einstein  Scalar  occurs  on  nearly  every  page. 
Tolman's  excellent  work  is,  in  the  main,  an  exposition  of  the 
Einstein  and  Minkowski  theories  of  relativity. 

The  Minkowski  theory  is  a  case  of  four-dimensional 
vector  analysis.  The  whole  theory  of  relativity  is  therefore 
built  upon  and  around  this  Fundamental  Scalar  Relation. 
The  relativists  derive  this  relation  from  the  well  known 
Pythagorean  Theorem.  They  derive  their  basic  relation 
from  the  purely  geometrical  relations  which  pertain  to  a 
right  triangle.  These  purely  geometrical  relations  are  then 
imposed  upon  physical  phenomena.  The  results  are  often 
misinterpreted  because  of  their  confused  and  erroneous  no- 
tions concerning  space  and  time  which  have  led  them  into 
the  quagmires  of  an  unreal  four-dimensional  space.  It  is 
unfortunate  that  the  relativists  are  not  philosophers  now 
that  they  have  been  forced  into  this  field  which  science  has 
vainly  attempted  to  belittle  by  inuendo  and  ridicule. 

The  writer  has  derived  this  Fundamental  Scalar  directly 
from  those  basic  relations  of  interaction  which  constitute  the 
norms  of  his  Theory  of  Interdependence.  The  author  de- 
velops this  important  Scalar  directly  from  the  fundamental 
laws  of  action  whereas  the  relativists  develop  it  from  a 
purely  geometrical  relation  whose  connection  with  action  is 
thereafter  sought.  The  method  used  by  the  relativists  is 
replete  with  possibilities  of  misinterpreting  the  significance 
and  genuineness  of  the  hoped  for  connections  between  this 


280  SCIENTIFIC  THEISM 

purely  geometrical  relation  and  actual  physical  action.  The 
author  has  shown  in  the  above  the  real  significance  of  this 
scalar  as  an  Interaction  Coefficient. 

The  following  subsidiary  relations  may  readily  be  de- 
duced from  the  foregoing  : 

n          (n  -f  a)      n  ,  .     /n  \      /n  \      ve 

—  =  -  —  —  —  -  ;  —  =  a(n  -f  a)  ;  (  —  )^-  (  -  )  =  —  =  an. 
v.  n  vc  \vj     \vj     vc 

)^      /(an)2   (n  -f  a) 

"" 


2U,  /(n  +  a).,  /(n2—  a2)^      / 
"V     (n-a)'V      v*         "V 


vfl  (n-a)'  v*  (n-a) 


4/(n2—a2)  _._     4/(n2—  a2) 


149.    The  Basic  Fallacy  of  Relativity. 

Tolman,  in  the  work  cited  above  (page  30),  makes  the 
following  statement  :  "We  thus  find  that  two  observers,  A 
and  B,  who  are  in  relative  motion  will  not  in  general  agree 
in  their  measurements  of  the  time  interval  necessary  for  a 
given  event  to  take  place."  He  states  further  that  time  in- 
tervals made  with  a  moving  clock  must  be  multiplied  by  the 
"Einstein  Scalar"  in  order  to  agree  with  measurements 
made  with  a  stationary  system  of  clocks. 

A  complete  web  of  confusions  has  grown  about  this 
primary  and  basic  confusion  of  relativity.  The  Tolman  ref- 
erence deals  with  the  geometrical  relations  which  pertain 
to  the  sides  of  a  right  triangle  as  stated  by  the  Pythagorean 
Theorem. 

The  whole  matter  hinges  upon  our  interpretation  of  the 
geometrical  relations  which  hold  for  the  right  triangle  ABC, 
whose  hypotenuse  is  AB,  in  conjunction  with  the  velocity  of 
light.  The  triangle  ABC,  according  to  the  relativists,  con- 
tains the  relativity  norms  for  a  moving  system  when  com- 
pared with  the  single  normal  line  EC.  In  this  moving 
system  ABC  the  base  of  the  triangle,  that  is  AC  indicates  the 
direction  of  the  motion  of  the  moving  system  ABC.  The 
relativists  argue  that  for  a  stationary  observer  the  path  of 
a  light  ray  reflected  from  a  mirror  parallel  to  AC  in  the  mov- 
ing system  ABC  would  be  given  by  the  hypotenuse  AB  in- 
stead of  by  the  normal  BC  to  the  mirror.  There  arises  there- 
fore, they  contend,  a  genuine  relativity  of  time  which  must 


SCIENTIFIC  THEISM  281 

be  taken  account  of  whenever  a  stationary  observer  at- 
tempts to  make  time  measurements  of  a  moving  system. 
From  the  Pythagorean  Theorem  the  relativists  conclude 
that: 


'  -i       ^C)-j,andB       -   -  /•         (AC); 


(AB)'  (AB)3'      "AB          V         "(AST1* 

The  conclusion  is,  according  to  the  relativists,  that  it  ap- 
parently takes  a  longer  time  for  the  same  experiment  in  the 
moving  system  than  in  the  stationary  system  when  both 
times  are  measured  by  the  stationary  observer.  If  the  sta- 
tionary observer  finds  that  the  experiment  in  the  moving 
system  is  performed  in  1  second  then  the  same  experiment 
performed  in  his  stationary  system  will  only  require  that 
portion  of  a  second  which  is  expressed  by  the  Einstein 
Scalar,  that  is, 


-         (AC)2     , 

1  —  (ATO*  of  a  second. 

For  this  reason  we  must  turn  the  whole  world  topsy- 
turvy; clocks  must  be  properly  set  in  moving  systems,  and 
space  must  be  suitably  "warped"  in  order  to  allow  for  these 
relativistic  distortions.  A  further  relief  from  this  cosmic 
pandemonium  may  be  had  through  the  use  of  the  relativistic 
panacea  known  as  the  fourth-dimension  which  is  capable  of 
warping  and  distorting  reality  to  a  degree  satisfactory  to 
the  most  exacting  mathematician. 

The  relativists  have  placed  a  most  curious  misinterpre- 
tation upon  the  alleged  relations  between  stationary  and 
moving  systems.  We  find  Hermann  Minkowski  attempting 
a  synthesis  of  space  and  time  into  a  basic  unitary  world 
tetrad  masquerading  as  a  four-dimensional  reality. 

Let  us  inquire  into  the  real  significance  of  the  results 
of  the  two  experiments  cited  above.  We  at  once  admit  that, 
with  the  velocity  of  light  constant,  the  times  required  to 
traverse  two  paths  of  unequal  length  will  be  unequal.  A 
greater  time  period  will  be  required  for  the  longer  path. 
In  this  there  is  nothing  remarkable.  In  fact  it  is  nothing 
other  than  would  be  dictated  by  common  sense  which  is 
and  always  has  been  a  rare  intellectual  jewel.  If  the  path 
of  a  ray  of  light  be  along  the  hypotenuse  AB  of  a  right 


282  SCIENTIFIC  THEISM 

triangle  then  the  time  required  to  traverse  this  path  will 
be  longer  than  the  time  required  to  make  the  traverse  over 
the  normal  line  BC  of  the  same  right  triangle  because  the 
hypotenus  AB  is  longer  than  the  altitude  BC  of  the  same 
right  triangle.  This  is  true  irrespective  of  the  method  em- 
ployed in  causing  a  ray  of  light  to  travel  over  these  two 
paths.  It  is  equally  true  for  both  the  stationary  and  the 
moving  system.  Moreover  the  stationary  observer  can  ar< 
range,  by  a  suitable  disposition  of  the  source  of  light,  to 
exactly  reproduce  both  experiments.  Since  light  is  a  mate- 
rial system  it  is  evident  that  it  will  be  subject  to  the  re- 
sultant effects  of  the  interacting  intensities.  Therefore 
if  the  velocity  of  the  moving  system  is  commensurate 
with  the  length  AC  of  the  base  of  the  triangle  we  must 
expect  the  resultant  path  of  the  ray  of  light  to  be  modified 
accordingly.  In  other  words,  the  path  of  the  ray  will  be 
AB  and  not  BC.  The  resulting  path  AB  is  therefore  due  to 
the  simultaneous  action  of  two  vectorial  intensities  com- 
mensurate with  the  velocity  of  light  and  the  velocity  of 
translation  of  the  moving  system.  The  stationary  observer 
can  arrange,  by  a  suitable  disposition  of  the  source  of  light 
in  relation  to  a  proper  location  of  his  point  of  observation, 
to  reproduce  the  magnitude  involved  in  the  moving  system. 
There  will  be  no  difference  in  the  results  produced.  The 
only  difference  will  be  in  the  method  of  producing  these 
results.  Therefore  he  may  derive  the  same  inferences  from 
the  stationary  system,  by  a  new  distribution  of  the  elements 
of  the  experiment,  as  may  be  derived  from  his  observation 
of  the  moving  system.  Moreover,  it  is  futile  for  him  to 
attempt  to  measure  the  time  of  traverse  of  the  normal  ray 
BC  in  the  moving  system,  because  the  fact  of  motion  pre- 
cludes all  possibility  of  making  such  measurement.  Further- 
more, unless  light  was  an  instantaneous  phenomenon,  re- 
quiring no  time  for  its  propagation,  an  observer  located 
upon  the  moving  system  would  find  it  impossible  to  pro- 
duce a  normally  reflected  ray  from  a  light  source  regarded 
as  a  fixed  point. 

It  is  therefore  evident  that  the  stationary  observer  has 
not  and  cannot  observe  a  normally  reflected  ray  (BC)  in 
a  moving  system  ABC.  What  he  can  observe  is  the  result- 
ant path  and  its  time  period.  This  resultant  path  is  along 


SCIENTIFIC  THEISM  283 

the  hypotenuse  AB  and  since  this  is  longer  than  the  normal 
BC  the  time  period  of  the  former  will  be  longer  than  the 
time  period  of  the  latter  provided  that  the  velocity  of  light 
is  constant  which  is  here  assumed.  By  knowing  the  velocity 
of  the  moving  system  he  can  duplicate  the  involved  vectorial 
magnitudes  upon  his  stationary  system.  Therefore  he  need 
not  concern  himself  at  all  with  the  complicated  readjust- 
ment and  setting  of  clocks  in  order  to  derive  correctly  all 
the  inferences  which  can  be  derived  from  both  experiments. 
In  fact  he  did  not  measure  the  time  for  the  normal  path  BC 
in  the  moving  system  but  he  measured  the  time  element  in- 
volved in  a  totally  different  path,  that  is,  the  hypotenuse  AB 
of  the  moving  system  ABC.  This  time  element  he  can  more 
easily  measure  on  his  own  stationary  system  by  a  proper 
readjustment  of  his  experiment  in  a  manner  allowing  for 
the  velocity  of  the  moving  system. 

The  relativists  have  therefore  rediscovered  the  astound- 
ing facts  that,  1st,  it  takes  light  a  longer  time  to  traverse  a 
longer  path  than  it  does  to  traverse  a  shorter  path;  and 
2nd,  they  have  also  found  that  the  old  Pythagorean 
Theorem  is  a  means  of  finding  the  relative  lengths  of  the 
sides  of  a  right  triangle.  Because  of  these  astounding  dis- 
coveries we  are  requested  to  accept,  without  protest,  a  new 
relativistic  science  built  upon  the  quicksands  of  non-Eucli- 
dean geometry.  Be  it  noted  that  they  used  Euclidean 
geometry  in  deriving  their  basic  relation. 

Utter  confusion  reigns  amongst  the  relativists  in  regard 
to  their  notions  of  the  significance  of  space  and  time.  For 
them  space  and  time  arise,  as  it  were,  from  some  super- 
mundane single  essence  abiding  in  the  fourth-dimension. 
This  single  essence  is,  however,  a  tetrad  capable  of  a  four- 
way  subdivision  into  coordinates  conforming  with  the  appe- 
tite of  their  four-dimensional  Frankenstein.  The  relativists 
have,  however,  rendered  mankind  a  great  service  in  bring- 
ing forcibly  before  the  world  the  general  notion  of  relativity 
despite  the  fact  that  they  have  so  grossly  misinterpreted 
the  real  significance  of  their  theory. 

In  his  Theory  of  Interdependence  the  writer  has  shown 
that  space  and  time  are  two  distinct  forms  of  apprehension, 
just  as  distinct  as  two  separate  particles  of  matter.  Never- 
theless, they  are  no  more  distinct  than  two  particles  of 


284  SCIENTIFIC  THEISM 

matter  because  all  particles  of  matter  are  interdependent 
in  their  physical  manifestation.  Space  and  time,  although 
not  identities  possess  interdependent  significance  in  the 
interpretation  of  all  the  manifold  types  of  activity. 

We  have  shown  in  the  above  that  the  Fundamental 
Scalar  of  Relativity  has  its  real  origin  and  root  in  inter- 
action from  which  it  can  be  derived  directly  without  the 
subterfuge  of  a  mere  geometrical  relation.  We  have  further 
shown  that  the  vectors  of  interdependent  motion  may  be  re- 
lated to  the  vectors  of  independent  motion  by  vectorial  com- 
ponents indicating  transverse  and  longitudinal  interaction 
intensities,  describable  geometrically  by  means  of  a  right 
triangle  which  involves  the  author's  Interaction  Coefficient 
which  is  identical  in  its  algebraic  value  with  the  Scalar  of 
Relativity.  Its  real  significance,  however,  appears  in  the 
writer's  Theory  of  Interdependence.  The  relativists  have 
failed  utterly  in  their  attempt  to  relate  this  Scalar  to  genu- 
ine activity. 

150.     Further  Criticism  of  the  Theory  of  Relativity. 

Einstein  first  outlined  the  preliminary  postulates  of 
relativity  in  a  paper  which  appeared  in  Annalen  der  Physik, 
in  1905.  In  this  paper  he  considered  the  meaning  of  events 
occurring  in  different  locations.  We  have  it  on  the  authority 
of  his  disciple,  Professor  A.  S.  Eddington,  that  Einstein's 
theory  of  gravitation,  which  follows  as  a  consequent  of  his 
theory  of  space  and  time,  was  formulated  sometime  during 
the  year  1915  (see  Professor  Eddington's  article  entitled 
"Einstein's  Theory  of  Space  and  Time"  in  The  Contem- 
porary Review  of  December,  1919,  page  640) . 

Sir  Oliver  Lodge  pertinently  criticises  the  Theory  of 
Relativity  in  a  paper  entitled  "The  New  Theory  of  Gravity" 
which  appeared  in  the  December  issue  of  the  Nineteenth 
Century  and  After  (see  pages  1195,  1196,  1199,  and  1200) . 
We  quote  the  following  from  this  paper : 

"The  theory — further  developed  by  Minkowski  in  1908, 
and  adopted  or  modified  by  de  Sitter,  Silberstein,  Eddington, 
and  others  later — lays  its  hands  not  only  on  ether  and 
matter,  on  light  and  gravitation,  but  attacks  the  fundamen- 
tal conceptions  of  Space  and  Time  also.  It  evolves  a  gen- 
eralized theory  of  gravity  to  which  the  Newtonian  theory 


SCIENTIFIC  THEISM  285 

is  a  close  approximation.  It  attributes  inertia  to  energy 
(not  for  the  first  time).  It  gives  a  theory  of  Space  of 
which  Euclidean  space  may  be  regarded  as  a  special  case. 
It  involves  a  theory  of  Time  which  may  be  described  as 
requiring  four  co-ordinates  instead  of  three,  to  fix  a  posi- 
tion, and  virtually  making  Time  an  aspect  of  a  fourth 
dimension  of  Space.  The  timing  of  events  on  this  theory 
becomes  extremely  complicated;  it  is  barely  possible  to  say 
even  when  two  events  are  simultaneous,  or  to  offer  a 
criterion  as  to  what  is  meant  by  simultaneity.  Gravitation 
becomes  a  property  of  Space — of  four-dimensional  Time- 
Space — it  therefore  affects  everything  that  occurs  in  space. 
There  are  ten  possible  coefficients  instead  of  the  common 
quality  g,  the  intensity  of  gravity.  A  ray  of  light  is  not 
straight ;  the  path  of  "least  action"  is  affected  by  a  gravita- 
tional field,  which  acts  like  a  change  in  optical  density  and 
so  causes  a  sort  of  refraction.  Also  the  frequency  of  light- 
vibrations  is  reduced  by  the  neighborhood  of  a  massive 
body.  The  first  law  of  motion,  even,  requires  re-wording, 
since  gravity  is  not  a  force  but  a  property  of  'crumpled* 
Space.  The  theory  of  relativity  is  a  limitation,  and  at  the 
same  time  a  complication,  of  human  knowledge." 

Continuing  on  pages  1199,  and  1200,  Sir  Oliver  Lodge 
states,  "But  the  'warp'  idea  gives  us  a  weird  kind  of  infinity 
that  simulates  some  of  the  properties  of  finiteness;  Space 
could  never  be  transcended,  we  should  never  arrive  at  a 
boundary  wherever  we  start  and  however  far  we  travel,  and 
yet  our  environment  would  not  be  exactly  what  we  have  tried 
to  conceive  as  infinite." 

"The  present  writer,"  Sir  Oliver  Lodge  says,  "holds  it 
dangerous  to  base  such  far-reaching  consequences,  even  if 
anything  like  them  can  legitimately  be  drawn — which  is 
doubtful — on  a  predicted  effect  which  may  after  all  be 
accounted  for  and  expressed  in  simpler  fashion.  Our  admi- 
ration for  the  brilliant  way  in  which  the  fact  was  arrived 
at  must  not  make  us  too  enthusiastically  ready  to  assimilate 
the  whole  complicated  theory  out  of  which  it  arose.  So 
far  as  the  present  writer  understands  the  theories  of  Ein- 
stein and  Minkowski,  he  does  not  feel  compelled  to  admit 
an  essential  warp  or  twist  in  Space." 

This  splendid  criticism  of  the  Theory  of  Relativity  is  in 


286  SCIENTIFIC  THEISM 

complete  harmony  with  the  author's  views  expressed  in  the 
above.  The  author  severely  criticised  the  vaporous  specula- 
tions of  the  non-Euclidean  geometers  in  his  paper  "The 
Atom  of  Electrochemistry"  which  apeared  in  1902.  Now 
the  relativists  are  attempting  the  erection  of  a  new  scientific 
structure  upon  the  quagmires  of  non-Euclidean  speculations 
concerning  unreality. 

The  writer  again  wishes  to  record  his  vigorous  protest 
against  this  "undignified  nonsense"  and  he  herewith  reiter- 
ates his  plea  for  a  return  to  sanity  and  common  sense. 

151.     A  Brief  Criticism  of 

"Einstein's  Theory  of  Space  and  Time." 

Professor  Eddington,  in  his  article  "Einstein's  Theory 
of  Space  and  Time,"  referred  to  in  the  preceding  paragraph, 
states  the  following : 

"In  Einstein's  view,  since  the  space  (b)  is  not  revealed 
by  physical  measurements,  there  is  no  conceivable  reason 
for  believing  in  its  existence;  and  in  any  case  it  does  not 
concern  us.  Hence  for  him  space  is  always  and  solely 
measured  space.  We  cannot  predict  a  priori  what  will 
happen  to  measuring — appliances  in  a  strong  field  of  gravi- 
tation, hence  we  cannot  predict  what  kind  of  space  will  be 
there.  It  turns  out  that  it  is  probably  non-Euclidean,  or, 
as  it  is  popularly  expressed,  warped.  But  all  the  metaphysi- 
cal implication  disappears  when  we  remember  that  this  is 
merely  a  statement  about  the  unusual  behavior  of  measur- 
ing— appliances  in  unusual  circumstances." 

"The  reader  may  perhaps  think  that  it  is  a  bathos  that 
all  the  talk  of  the  warping  of  space  should  come  to  nothing 
more  than  this ;  but  he  must  remember  that  the  space  that 
is  warped  is  actually  the  space  of  perception.  The  judg- 
ments of  his  senses  are  physical  measures,  though  crude; 
and  the  applicances  of  the  laboratory  merely  assist  and 
refine  these  judgments  without  altering  their  character. 
We  are  inclined  to  overlook  the  channel  of  sense-measures 
by  which  external  nature  is  presented  to  the  mind,  and  to 
think  that  in  some  way  the  mind  is  directly  acquainted  with 
things  outside  us.  So  far  from  this  being  true,  two  of  the 
most  essential  features  in  our  mental  picture  of  the  external 
world — viz.,  space  and  time,  are  not  actually  in  the  external 


SCIENTIFIC  THEISM  287 

world,  but  are  introduced  into  the  picture  in  the  course  of 
transmission  through  sense-channels  to  our  brains." 

"In  every  observation  the  observer  has  a  share  as  im- 
portant as  that  of  the  thing  which  is  observed.  With  the 
observer  I  include  any  measuring-apparatus  he  may  use  to 
improve  the  judgments  of  his  sense.  Einstein's  achievement 
is  a  separation  of  the  shares  of  the  observer  and  of  external 
nature  far  more  complete  than  hitherto,  and  opposed  to  the 
separation  which  through  long  generations  we  have  in- 
stinctively adopted.  He  assigns  space  and  time  solely  to 
the  observer;  in  nature  there  is  left  something  which  for 
want  of  a  better  name  we  may  call  space-time.  In  a  sense 
it  is  a  combination  of  space  and  time,  but  it  has  lost  the 
more  familiar  qualities  of  both.  It  arouses  curiosity  because 
it  has  four  dimensions." 

"The  observer  himself  is  in  nature  and  he  is  passing 
through  this  four-dimensional  'something.'  Let  us  see 
what  he  makes  of  it.  He  is  sitting  in  his  armchair  making 
no  conscious  effort  to  change  position ;  nevertheless,  he  per- 
ceives that  he  is  not  stationary  in  the  great  world — he  is 
progressing  along  time.  He  makes  a  conscious  effort  and 
walks  about  the  room;  now  he  is  progressing  in  space. 
Thus  he  splits  up  this  four-dimensional  thing ;  that  direction 
in  which  he  progresses  without  conscious  effort  is  time, 
other  directions  are  space." 

"Relegating  space  and  time  to  their  proper  source — the 
observer — Einstein  bids  us  contemplate  the  residuum  of 
what  we  observe.  This  residuum  is  the  true  world.  It  is 
shapeless,  because  we  have  abstracted  space ;  yet  it  is  metri- 
cal and  has  quantitative  properties  which  can  be  expressed 
in  mathematical  terms.  Clearly  we  cannot  describe  this 
true  world  in  terms  of  familiar  things,  because  the  whole 
point  of  Einstein's  theory  is  that  we  must  abstract  the  ideas 
which  we  ourselves  have  added  in  order  to  form  familiar 
things.  Further,  the  laws  of  nature  must  relate  to  this 
four-dimensional  residuum,  and  the  space  and  time  we  our- 
selves introduce  cannot  be  relevant.  This  led  Einstein  to 
the  conclusion  that  Newton's  law  of  gravitation,  which 
refers  to  one  particular  separation  of  space  and  time,  cannot 
be  the  exact  law ;  and  he  proposed  a  new  law  applicable  to  a 


288  SCIENTIFIC  THEISM 

four-dimensional  world,  which  has  now  been  strikingly  jus- 
tified by  observation." 

The  above  excerpts  from  Professor  Eddington's  article 
constitute  an  able  an  concise  summary  of  the  pseudo-meta- 
physical position  of  Einstein.  We  shall  now  critically  con- 
sider the  various  contentions  set  forth  in  the  preceding  sum- 
mary of  Einstein's  position. 

We  are  told  that  since  space  is  not  revealed  by  physical 
measurements,  there  is  no  conceivable  reason  for  believing 
in  its  existence.  Is  that  interaction  phase  known  to  science 
as  energy  revealed  by  physical  measurement?  It  is  revealed 
no  more  and  no  less  than  space  is  by  physical  measurement. 
As  an  independent  tentity  moving  about  the  physical  uni- 
verse it  is  not  revealed  by  any  physical  observation.  What 
we  observe  are  changes  and  transformations  in  material 
systems.  We  have  never  been  able  and  never  will  be  able 
to  isolate  energy  as  an  independent  existence.  Nevertheless 
the  term  energy  is  a  scientific  admission  that  a  genuine 
activity  principle  exists  which  accounts  for  the  actuality  of 
physical  phenomena.  No  scientist  can  sanely  deny  the 
existence  of  this  actuating  principle  upon  the  meagre 
grounds  that  he  has  not  been  able  to  isolate  it  by  means 
of  measuring-appliances.  If  the  relativists  elevate  energy 
to  a  position  of  independence  what  then  becomes  of  their 
alleged  theory  of  relativity?  It  no  more  follows  that  because 
science  has  not  been  able  to  isolate  the  forms  of  apprehen- 
sion, space  and  time,  therefore  both  are  non-existent.  Their 
actuality  is  revealed  through  interaction  of  subject  and 
object.  The  activity  principle  is  also  revealed  to  the  sub- 
ject by  observations  of  the  changes  in  the  objective  world. 

We  are  also  informed  that  it  is  impossible  to  predict  a 
priori  what  will  happen  to  measuring-appliances  in  a  strong 
field  of  gravitation,  hence  we  cannot  predict  what  kind  of 
space  will  be  there.  It  turns  out,  we  are  told,  that  it  is 
probably  non-Euclidean,  or,  as  it  is  popularly  expressed, 
warped.  If  something  happens  to  the  measuring-appli- 
ances, if  they  are  warped  or  deformed,  we  naturally  inquire 
into  the  cause  of  this  change.  Einstein  and  Eddington, 
judging  from  Eddington's  statements  quoted  above,  rush  to 
the  conclusion  that  space  is  non-Euclidean  or  warped.  Do 
they  mean  to  tell  us  that  space  is  an  activity  principle  capa- 


SCIENTIFIC  THEISM  289 

ble  of  warping  the  measuring-appliances?  Possibly  time 
did  the  warping. 

Why  refer  to  the  "strong  field  of  gravitation"  at  all  if 
space  or  time  were  at  the  bottom  of  the  warping  phenome- 
non? Perhaps  the  strong  field  of  gravitation  first  warped 
space  which,  in  turn,  was  then  able  to  warp  the  measuring- 
appliances.  Of  course  it  may  be  that  the  non-Euclidean 
warped  space  created  the  strong  gravitational  field  which 
then  affected  the  instruments.  The  final  possibility  is  that 
the  measuring-appliances  themselves  caused  a  general  cos- 
mic disturbance  which  retaliated  by  inflicting  a  warped 
condition  on  the  cause  of  the  disturbance. 

From  these  possibilities  the  relativists  arbitrarily  select 
one  possibility,  that  is,  warped  space,  because  this  fits  in 
with  their  mathematcal  speculations.  Instead  of  forcing 
mathematics  to  conform  with  and  truly  represent  reality, 
unreality  must  exist  because  it  conforms  with  mathematical 
speculation.  Non-Euclidean  space  is  merely  a  product  of 
mathematical  imagination.  It  has  no  genuine  reality  other 
than  conceptual.  Nevertheless  the  relativists  insist  that  the 
physical  world  must  conform  to  this  distorted  and  warped 
creature  of  their  imagination.  Mathematics  is  an  a  priori 
science  grounded  in  depths  of  logical  conscious  life. 
Euclidean  geometry  conforms  with  the  requirements  of  this 
logical  mental  life.  It  also  conforms  with  the  requirements 
of  the  external  world  which  is  three-dimensional.  This  is 
true  because  there  is  genuine  interaction  between  the  con- 
scious and  the  unconscious  world  which  are  interdependent. 
Space  and  time  therefore  are  not  only  of  the  subject  but 
they  are  rooted  in  the  depths  of  reality  and  because  there 
is  interaction  and  interdependence  in  the  unitary  cosmos 
therefore  the  mental  world  of  Euclidean  or  three-dimen- 
sional properties  agrees  with  the  physical  and  external 
world.  The  non-Euclidean  or  four-dimensional  world  is 
an  imaginary  world  based  upon  assumptions  which  have  no 
genuine  counterpart  in  the  real  physical  world.  The  mills 
of  mathematical  logic  grind  with  unerring  truth  and  pre- 
cision but  the  machinery  of  mathematics  neither  creates 
nor  guarantees  that  its  resulting  products  represent  reality 
truly.  The  assumptions  that  are  introduced  into  the  in- 
fallible mathematical  machine  must  be  absolutely  truthful 


290  SCIENTIFIC  THEISM 

representations  of  reality  if  the  resulting  products  are  to  be 
labeled  true  and  real. 

The  attempt  of  the  relativists  to  merge  space  and  time 
into  a  "root  entity"  which  they  name  "space-time"  and 
which  is  supposed  to  be  a  four-dimensional  reality  fails 
completely  because  of  the  insuperable  difference  between 
extension  and  duration.  The  distinction  between  space  and 
time  exists  in  the  very  foundations  of  the  cosmos.  If  this 
distinction  did  not  exist  in  the  objective  would  it  could 
never  become  known  to  the  conscious  subjective  world  for 
the  reason  that  space  and  time  are  not  mere  concepts  but 
they  are  genuine  elements  of  reality.  Therefore  the  observer 
does  not  "split  up  this  four-dimensional  thing"  as  Einstein 
and  Eddington  maintain.  Moreover,  neither  space  nor  time 
is  a  thing  and  consequently  any  alleged  amalgamation  of  the 
two  cannot  be  termed  a  thing.  Furthermore  we  are  re- 
quested to  contemplate  the  world  residuum  after  we  have 
substracted  the  contributions  of  the  observer.  We  are  told 
that  the  remainder  is  the  true  world  and  that  it  is  shapeless. 
Einstein  thus  presents  us  with  a  modern  revision  of  the 
thing-in-itself  of  Kant  with  the  profound  philosophical  in- 
sight of  Kant  totally  absent  from  his  four-dimensional 
intellectual  product.  We  have  pointed  out  the  fallacies  in 
the  Kantian  thing-in-itself  in  preceding  paragraphs.  The 
same  criticisms  hold,  for  this  modern  unphilosophical  per- 
version. Eddington  is  careful  to  warn  us  that  "all  the  meta- 
physical implication  disappears  when  we  remember  that  this 
is  merely  a  statement  about  the  unusual  behavior  of  measur- 
ing-appliances in  unusual  circumstances."  Why  then,  we 
ask,  bring  into  the  argument  this  pseudo-metaphysical  four- 
dimensional  space  creature  which  is  assumed  capable  of 
producing  "warped"  acts?  If  an  iron  rod  expands  under 
the  influence  of  heat  why  attribute  this  change  to  the 
activity  of  a  "warped  space"  which  is  neither  an  action 
agent  nor  a  thing?  Why  not  admit  that  common  sense  is 
correct  in  assigning  the  cause  of  this  change  in  length  of 
the  iron  rod  to  the  presence  of  a  real  activity  principle? 
Similarly  we  demand  that  if  measuring-appliances  undergo 
a  change  in  "a  strong  field  of  gravitation"  then  the  cause 
of  this  change  is  to  be  found  in  the  activity  intensities  in- 
volved in  the  gravitational  field  and  not  in  a  fictitious  warped 


SCIENTIFIC  THEISM  291 

space  which  is  neither  action  agent  nor  thing.  The  result 
of  interaction  may  be  in  part  described  in  terms  of  space  (of 
three  dimensions)  and  time  but  space  and  time  are  not  the 
causes  of  any  physical  change  whatsoever. 

The  inadvertent  invasion  of  the  realm  of  philosophy  and 
metaphysics  by  the  relativists  constitutes  a  monumental  in- 
dication of  the  necessity  of  a  complete  revision  of  the  rela- 
tive values  of  the  various  branches  of  knowledge.  One  may 
say  that  in  a  day  an  intellectual  revolution  has  been  accom- 
plished. Science  has  been  forced  to  incorporate  philosophy 
into  its  scheme  of  things.  Metaphysics  has  become  an  in- 
tegral part  of  physics.  Although  these  first  philosophical 
attempts  of  the  relativists  resemble  the  first  efforts  of  a 
child  to  walk,  nevertheless  they  deserve  commendation  be- 
cause they  indicate  emancipation  from  the  scientific  bias  of 
the  past.  From  now  on  philosophy  and  metaphysics  must 
be  regarded  as  the  foundation  upon  which  the  future  edifice 
of  science  must  rest.  No  serious  student  of  science  can  now 
afford  to  ignore  philosophy  and  metaphysics.  Upon  this 
foundation  the  new  science  will  become  a  crystal  through 
which  mankind  may  see  God, 


INDEX  TO  AUTHORS 

N.  B. — The  figures  refer  to  the  numbered  paragraphs 


Ampere,  39 
Armstrong,  H.  E.,  112 
Avogadro,  41 

Beltrami,  110 

Berkely,  64 

Bernoulli,  Daniel,  18,  44 

Bessel,  126 

Bohr,  139 

Bolyai,  110 

Boscovich,  18,  22,  39,  44,  57,  80 

Bruno,  39 

Campbell,  N.  R.,  54 
Cayley,  110 
Coulomb,  56 

Dalton,  40 
Delboeuf,  110 
Democritus,  39 
Descartes,  44 

Eddington,  150,  151 
Einstein,  Albert,  109,  138, 

Table  V,  150,  151 
Engel,  110 
Euclid,  110 
Euler,  49 

Faraday,  20,  39 
Fechner,  39 
Fitzgerald,  G.  F.,  112 

Gauss,  110 
Grassmann,  110 

Halsted,  110 
Heaviside,  18 
Hegel,  39,  67 
Helmholtz,  49,  82,  110 
Heracleitus,  39,  67 
Hertz,  46 

Kant,  39,  66,  67 

Kaufmann,  18,  41,  58,  79,  108, 

132,  138 
Kelvin,  49,  82 
Kepler,  95,  96,  99,  126 
Klein,  110 


Laplace,  39 

Leibnitz,  39 

Leucippus,  39 

Lie,  Sophus,  110 

Lobatchevsky,  110 

Lodge,  Sir  Oliver,  150 

Lorentz,  76,  108,  138,  Table  V 

McDougall,  55 
Mach,  110 

Maxwell,  Clerk,  46,  47 
Mellor,  J.  W.,  112 
Michelson,  A.  A.,  108 
Millikan,  R.  A.,  107,  132,  139 
Minkowski,  148,  150 
Mosotti,  53 

Nagaoka,  109 
Newcomb,  110 

Newton,  7  (Synopsis),  94,  96, 
101 

Parmenides,  39 
Pearson,  Karl,  50 
Poincare,  108,  110,  111 
Poisson,  53 

Riemann,  110 

Russell,  110 

Rutherford,  Sir  E.,  18,  109 

Schopenhauer,  66 
Searle,  18 
Spinoza,  67 
Stevinus,  59 
Stackel,  110 
Swedenborg,  39 

Thales,  39 

Thomson,  Sir  J.  J.,  12,  13,  18, 

20,  79,  107,  109,  132 
Tolman,  148,  149 

Varley,  79 
Voltaire,  44 

Wilson,  H.  A.,  107,  132 


293 


INDEX  TO  SUBJECT 

N.  B. — -The  figures  refer  to  the  numbered  paragraphs 


Absolute,  82 

freedom,  124 

reality,  18   (Synopsis),  122 

truth,  124 
Acceleration,  5,  9 

phase,  62 
Accident,  92 
Action,  61 

phase,  62 
Action  at  a  distance,  13,  18, 

21,  44 

Activity  principle,  9 
Ascending  processes,  30,  112 
Atheism,  91 
Atom,  17  (Synopsis),  13,  40 

divisibility  of,  19 

structure  of  Bohr's,  139 

structure  of  Nagaoka's,  109 

structure    of    Rutherford's, 
109 

structure  of  Space-Time 

Potential,  109,  139 

structure     of     Thomson's, 

20,  109 

Atomic  masses,  132,  Table  IV 
Atomic     mass     moduli,     132, 

Table  III 
Avogadro's    constant,    140, 

Table  VI 
Beta  rays,  41,  79 
Cartesian  development  of  Kep- 

lerian  Laws,  96 
Categories  of  reality,  122 
Causes,  primary  and  second- 
ary, 89 

Cell  action,  112 
Central    forces    according    to 

Poincare,  111 
Chance,  123 
Change  point,  104,  129 
Chaos,  8 


Charge  e,  107 

calculated  by  the  Primary 
Functions  of  Space-Time 
Potential,  132 

calculated  by  the  Secondary 
Functions  of  Space-Time 
Potential,  134 
Chemically   equivalent  atomic 

masses,  132,  Table  II 
Closed  chain  of  concepts,  6,  10, 

22 

Concepts  of  science,  59 
Conceptual  bridges,  failure  of, 

16 
Concurrent  system,  29,  61,  77, 

82,  86 

in  conjunction  with  excitant 
system  as  basis  of  phe- 
nomena of  light  and  elec- 
tric oscillations,  108 

materialization  of,  80 
Conscious  and  unconscious 

world,  121 

Conscious   centers,   character- 
istics of,  122 
Conscious  world,  120 
Constants,  developed  from  the 

Space-Time  Potential,  132 
Contact  in  space,  futile,  71 
Corpuscles,  negative,  20 
Cosmos,  8,  23, 
Cosmos  and  teleology,  23 
Cosmic  theories,  ancient,  39 
Daniell  cell,  114 
Deism,  91 

Descending  processes,  30,  112 
Deterministic     characteristics 

of  elementals,  43 
Dualism  of  science,  37 
Dynamic  equilibrium,  104 
Ecliptic,  its  obliquity,  100 

295 


296 


INDEX  TO  SUBJECT 


Electric  current,  80 
as  transformed  mechanical 

energy,  85 
Electric  field,  12 
Electrochemical  equivalent  per 

unit  valence,  132,  Table  II 
Electrolytic  ionization  accord- 
ing to  the  Space-Time  Po- 
tential, 137 
Electron,  30 
birth  of,  84 

theory     according     to     the 
Space-Time  Potential,  131 
Electrons,  flow  of,  80 
Empirical  position  of  science, 

7 

Energon,  28 
gyratory,  83 
three  phases  of,  30,  84,  112, 

114 

Energosial  or  concurrent  sys- 
tem, 82 
Energy,  5,  9 

of  electronic  repulsion,  96 
phase,  63 

English  Solar  Eclipse  Expedi- 
tion  (year  1919),  substan- 
tiating  theories    of    Space- 
Time  Potential,  141 
Entities  of  science,  two  alien, 

42 

Ether,  5,  44,  46,  50,  54,  75 
an  irrational  convenience  un 

known,  34 

and  materialism,  17 
assumed  capable  of  exerting 
pressure  on   moving  ele- 
mentals,  76 

critical  analysis  of  hypothe- 
sis, 52,  53 

criticism  of,  by  N.  R.  Camp- 
bell, 54 
inconsistent  content  of 

hypothesis,  51 
mathematical    myth,    6 

(Synopsis) 
mentiferous   of  McDougall, 

55 

real  purpose  of,  76 
Evolution,  failure  of  unifica- 
tion, 119 

Excitant  system,  29,  61,  86 
Extension,  88 


Fallacy  of  relativity,   149,   150, 
151 

Faraday  lines  of  force,  12 

Faraday  tubes,  20,  36 

Fatalism,  123 

Field  of  force,  its  implications, 
47 

Fields  of  interaction,  78 

Finite,  13 

Force,  5,  9,  35,  38 
center,  15,  22 
center  of  Boscovich,  57 
not  an  entity,  14 
phase  and  mass  phase,  62 
phase  and  space  form,  63 
phase  and  time  form,  63 

Free  choice,  123 

God,  1,  14,  21,  22 
Absolute  Reality,  122 
not  a  machinist,  23 
physical  proof  of  existence, 
24 

Gyratory  energons,  83 

Hyperbolic  function  of  the 
Space-Time  Potential,  102, 
103,  128 

Hyperbolic  logarithms,  cal- 
culations involving,  133 

Immanence,  22,  23,  58 

Immortality,  assurance  of,  124 
universality  of  belief  in,  124 

Impulse,  5 
phase,  63 

Infinite,  13,  23 

Influence  I,  not  a  force,  state, 
or  action,  70 
not  a  thing,  69 

Inorganic  centers,  character- 
istics of,  122 

Inorganic  world,  118,  122 

Instantaneous  dynamics,  93 

Interaction  coefficients,  145,  148 

Interdependence,  theory  of,  2, 
3,  4,  8,  11  (all  in  Synopsis), 
63,  67,  75,  78 

Interdependent  and  independent 
motion,  142,  143,  144,  146,  147. 

Inverse  first  power  variation, 
97 

Ionization  hypothesis,  critic- 
ism of,  112 

Ions  in  solution,  30 


INDEX  TO  SUBJECT 


297 


Interaction,  according  to  Bos- 
covich,  57 
fields  of,  78 
hypothesis  of,  67 
in  a  unitary  system,  63 
of    interdependent    centers, 

75 

Kaufmann  effect,  according  to 
the  Space-Time  Potential, 
138 

Keplerian  Laws,  as  developed 
by  the  Cartesians,  96 
as  developed  by  Newton,  95 
as  developed  by  the  Space- 
Time  Potential,  99,  126 
Kinetic  matter,  62 
Kinetic  reaction,  5 
Kinetic  reaction  phase,  62 
Kosmometer,  108 
Law  of  identity,  67 
Life  entity,  A  unity,  119 
Light,  case  of  interaction  be- 
tween  excitant   and   con- 
current systems,  15  (Syn- 
opsis), 28 

velocity  of,  is  the  limiting 
constant  of  relativity,  29, 
108 

Lines  of  force,  12 
Logarithmic   function   of  the 
Space-Time   Potential,   104, 

134 

Loremtz-Einste,in    Mass-Veloc- 
ity Relation,  138,  Table  V 
Macrocosm,  31,  104,  136 
Macrocosm ic  Relations,  105 
Mass,  5,  9 
and  the  ether,  20 
electromagnetic,  79 
not  constant,  29 
phase,  measurement  of,  62 
variation  with  velocity  ac- 
cording   to    Lorentz-Ein- 
stein,  108 

Mass-acceleration  center,  80 
Mass-acceleration  kern,  104 
variation  with  velocity  ac- 
cording    to     Space-Time 
Potential,  108 
Materialism,  91 
fallacious,  10,  11 
horror  for  vacuum,  22 
house  of,  21 


Materialistic  science,  concepts 
invalid,  3 

Mathematical  space,  distin- 
guished from  real  space,  110 

Mathematics,  a  critique  of,  33 

Matter,  5,  38,  61 
as  distinct  from  ether,  48 
as  ether  in  motion,  49 
can  it  act  where  it  is  not?. 

74 
electrical,  20 

Measurement,  physical,  62 

Mechanical  model,  1,  9 

Mechanism,  pure  is  futile,  2 

Metageometry  and  space,  110 

Microcosm,  31,  104,  136 

Microcosmic  relations,  105 

Millikan,  on  Bohr  atom,  139 

Model  of  physical  universe,  76 

Monism,  91 

Monon,  15,  27 
a  unity,  72 

essential  qualities  of,  S2 
negative  and  positive  nature 
of,  81 

Motion,  61 

transmission    of    according 
to  physics,  75 

Neutral  ionic  pairs,  112 

Newtonian,  conception  of 
universal  gravitation,  7 
(Synopsis) 

gravitational     relation     ac- 
cording to  dynamics,  127 
law  of  gravitation,  96 
relation,  critical  analysis  of, 

95,  96,  98 

relation,    its    discrepancy 
with  dynamics,  101 

Non-Euclidean  geometry,  110 

Non-Newtonian  dynamics,  93, 

94 

fundamental    functions    of, 
128 

Number,  incapable  of  account- 
ing for  cosmos,  14  (Synop- 
sis), 32 

Organic  centers,  122 

Organic  world,  119 

Pangeometry,  110 

Pantheism,  91 

Pearson,  Karl,  ether  hypothe- 
sis of,  50 

Perpetual  motion  impossible, 
59 


298 


INDEX  TO  SUBJECT 


Phases  of  matter,  122 

Physical  action,  68 

Physical  concepts,  relative,  60 

Physical  constants,  4  and  5  of 
Synopsis 

Physico-mathematical  rela- 
tions of  the  Space-Time  Po- 
tential, 135 

Planetary  orbits,  31 
according  to  the  Space-Time 

Potential,  99 

mathematical  development 
of  according  to  the  Space- 
Time  Potential,  125 

Positon,  30,  84,  85 

Potential  difference,  mainte- 
nance of,  58 

Potential  loci,  104 

Predetermination,  '123 

Primordial  activity  center,  27 

Primary  or  hyperbolic  func- 
tion of  the  Space-Time  Po- 
tential, 102,  103,  128 

Primary  matter,  80,  86,  122 
*  Primary  world,  122 

Purpose,  8,  92,  124 

Rational  world  order,  22 

Rationality  of  world,  faith  in,  8 

Reaction,  61 

Reason,  8 

Relative  reality,  18  (Synop- 
sis), 122 

Relativity,  a  physical  basis  of, 
29 
a  proof  of  the  Existence  of 

God,  59 
complete   physical   leads   to 

negation,  4  (Synopsis) 
concepts,  secondary,  63 
fallacy  of,  149,  150,  151 
of  Lorentz,  108 
of  Poincarg,  108 
of  the    Space-Time    Poten- 
tial, Synopsis  and  108 
ordinary  and  partial  theory 

of,  3  (Synopsis) 
physical,  futile,  18   (Synop- 
sis) 

Religious  intuition,  121 

Revelation,  91 

Rotary  systems,  130 

Scientific  renaissance,  79 

Secondary  or  logarithmic 
function  of  the  Space-Time 
Potential,  104,  134 


Secondary  matter,  80,  86,  122 
Selective  intelligence,   17,  36, 

43 

Skepticism,  absolute,  8 
Space,  6,  7,  9 

defined,  25 

not  unreal,  87 
Space-Time  Potential,  basic 

functions  of,  102 
Soul,  13  (Synopsis) 

a  unity,  119 

result  of  a  creative  act,  120 
Static  equilibrium,  104 
Statics    and    dynamics,    rela- 
tivity of,  93 

Subconscious  world,  117,  122 
Substance,  Spinoza  on,  67 
Substratum,  physical,  64,  65, 

66 

Teleology,  8,  92,  124 
Theism,  scientific,  91 
Thing-in-itself,  66 
Theoria  Philosophia  Natural- 
is,  18,  44 
Thought,  as  cognition,  120 

as  will,  120 
Time,  6,  7,  9 

defined,  26 
Transcendence,  58 

and  immanence,  91 

of  God,  physical  proof  of,  90 
Tubes  of  force,  12,  13,  36 
Unitary  system,  63 
Unity  of  things,  73 
Unknowns  of  science,  4 
Velocity,  5 

phase,  62 
Viton,  12  (Synopsis) 

the  life  ultimate,  119,  122 
Vortices  of  Descartes,  44 
Will,  of  Schopenhauer,  66 
World  of  subconsciousness,  117 
Worlds,  the  four,  116 
Work,  5 

done  in  a  cell  system,  113 

loci,  104 

loci,  relations  of  to  atomic 
structure,  139 

of  decomposition,  molecular, 
115 

phase,  63 

value,  relatively  definite  for 
each  point  in  space,  80 


LIBRARY 


000657739    9 


